diff --git a/src/lib/egraph/extractor/extractor_core.ml b/src/lib/egraph/extractor/extractor_core.ml
index 7c61a188..04b72215 100644
--- a/src/lib/egraph/extractor/extractor_core.ml
+++ b/src/lib/egraph/extractor/extractor_core.ml
@@ -91,6 +91,13 @@ let rec pp_ext ppf = function
     Format.fprintf ppf "(%a %a %a)" pp_prov p Enode.pp_op op
       (Format.pp_print_list ~pp_sep pp_ext) args
 
+(* Pure cost of an operation.
+
+   It's important to note that some of these costs are relative
+   to what we can rewrite the operation into. For example,
+   integer division/remainder has an enormous cost because we
+   want to incentivize rewrites a la Hacker's Delight.
+*)
 let op_cost : Enode.op -> cost = function
   | Oint (i, t) ->
     (* In practice, a negative constant might need some work to
@@ -116,7 +123,7 @@ let op_cost : Enode.op -> cost = function
   | Ovastart _ -> Cost.pure 0
   | Obr | Ovar _ -> Cost.pure 2
   | Osw _ | Obinop #Insn.bitwise_binop | Ounop _ -> Cost.pure 3
-  | Obinop (`div _ | `udiv _ | `rem _ | `urem _) -> Cost.pure 90
+  | Obinop (`div _ | `udiv _ | `rem _ | `urem _) -> Cost.pure 97
   | Obinop (`mul _) -> Cost.pure 42
   | Obinop (`mulh _ | `umulh _) -> Cost.pure 11
   | Obinop _ -> Cost.pure 4
diff --git a/src/lib/machine/x86/x86_amd64_common.ml b/src/lib/machine/x86/x86_amd64_common.ml
index 82b377a2..f62bae29 100644
--- a/src/lib/machine/x86/x86_amd64_common.ml
+++ b/src/lib/machine/x86/x86_amd64_common.ml
@@ -631,7 +631,7 @@ module Insn = struct
 
          This is morally equivalent to:
 
-         `x := cc ? b : a`
+         `a := cc ? b : a`
       *)
       ->
       Set.union (rset' [`rflags])
diff --git a/src/lib/magic_div.ml b/src/lib/magic_div.ml
index 96c102ad..5ed3e9ca 100644
--- a/src/lib/magic_div.ml
+++ b/src/lib/magic_div.ml
@@ -67,10 +67,11 @@ let signed d t =
         then B.(q2 + one, r2 - ad)
         else q2, r2 in
       let delta = B.(ad - r2) in
-      if Bv.(q1 < delta || (q1 = delta && r1 = zero)) then
+      if Bv.(q1 < delta || (q1 = delta && r1 = zero))
+      then loop p q1 r1 q2 r2
+      else
         let m = B.(q2 + one) in
-        (if B.msb d then B.neg m else m), p - sz
-      else loop p q1 r1 q2 r2 in
+        (if B.msb d then B.neg m else m), p - sz in
     let q1 = B.(mins / anc) in
     let r1 = B.(mins - q1 * anc) in
     let q2 = B.(mins / ad) in
diff --git a/src/lib/passes/simplify_cfg/simplify_cfg.ml b/src/lib/passes/simplify_cfg/simplify_cfg.ml
index 1b96cfd3..a8f39041 100644
--- a/src/lib/passes/simplify_cfg/simplify_cfg.ml
+++ b/src/lib/passes/simplify_cfg/simplify_cfg.ml
@@ -2,6 +2,7 @@ open Core
 open Virtual
 open Simplify_cfg_common
 
+module Ifc = Simplify_cfg_ifc
 module Brsel = Simplify_cfg_brsel
 module Merge_blks = Simplify_cfg_merge_blks
 module Contract = Simplify_cfg_contract
@@ -26,6 +27,7 @@ let run tenv fn =
       || Contract.run env
       || Short_circ.run env
       || Duplicate_br.run env
+      || Ifc.run tenv env fn
       || brsel
       then loop @@ recompute_cfg env @@ update_fn env fn
       else !!fn in
diff --git a/src/lib/passes/simplify_cfg/simplify_cfg_common.ml b/src/lib/passes/simplify_cfg/simplify_cfg_common.ml
index 7cc347b6..3e5239c2 100644
--- a/src/lib/passes/simplify_cfg/simplify_cfg_common.ml
+++ b/src/lib/passes/simplify_cfg/simplify_cfg_common.ml
@@ -42,14 +42,9 @@ let is_ret env l = match env.ret with
   | None -> false
 
 let update_fn env fn =
-  Func.blks fn |>
-  Seq.fold ~init:[] ~f:(fun acc b ->
-      let l = Blk.label b in
-      if Hashtbl.mem env.blks l then acc
-      else l :: acc) |>
-  Func.remove_blks_exn fn |>
-  Func.map_blks ~f:(fun b ->
-      Hashtbl.find_exn env.blks @@ Blk.label b)
+  Func.blks fn |> Seq.filter_map ~f:(fun b ->
+      Hashtbl.find env.blks @@ Blk.label b) |>
+  Seq.to_list |> Func.with_blks_exn fn
 
 let not_pseudo = Fn.non Label.is_pseudo
 
diff --git a/src/lib/passes/simplify_cfg/simplify_cfg_ifc.ml b/src/lib/passes/simplify_cfg/simplify_cfg_ifc.ml
new file mode 100644
index 00000000..a53edd29
--- /dev/null
+++ b/src/lib/passes/simplify_cfg/simplify_cfg_ifc.ml
@@ -0,0 +1,182 @@
+(* If-conversion canonicalization.
+
+   For the `Brsel` pass, we handle the "degenerate diamond"
+   case for if-conversion, where the join block is targeted
+   by both arms of the branch for our header block.
+
+   For other cases (e.g. a proper diamond, or a triangle),
+   we want to canonicalize the shape enough for other passes
+   to fire, so that `Brsel` can do the final part of if-conversion.
+*)
+
+open Core
+open Regular.Std
+open Virtual
+open Simplify_cfg_common
+
+module BR = Simplify_cfg_brsel
+
+type join =
+  | Diamond of {
+      pred1 : Label.t;
+      pred2 : Label.t;
+      hdr   : Label.t;
+    }
+  | Triangle of {
+      pred : Label.t;
+      hdr  : Label.t;
+    }
+
+let diamond p1 p2 h = Diamond {pred1 = p1; pred2 = p2; hdr = h}
+let triangle p h = Triangle {pred = p; hdr = h}
+
+let pp_join ppf = function
+  | Diamond {pred1; pred2; hdr} ->
+    Format.fprintf ppf "(diamond (hdr %a) (pred1 %a) (pred2 %a))"
+      Label.pp hdr Label.pp pred1 Label.pp pred2
+  | Triangle {pred; hdr} ->
+    Format.fprintf ppf "(triangle (hdr %a) (pred %a))"
+      Label.pp hdr Label.pp pred
+
+exception Not_hoistable
+
+let insn_cost : Insn.op -> int = function
+  (* Provably non-trapping div/rem gets a high cost. *)
+  | `bop (_, (`div #Type.imm | `rem #Type.imm), _, `int (i, _))
+    when Bv.(i <> zero) -> 4
+  (* Effectful or potentially trapping instructions cannot
+     be hoisted. *)
+  | `bop (_, (`div #Type.imm | `rem #Type.imm), _, _)
+  | `load _
+  | `store _
+  | #Insn.variadic
+  | `call _
+    -> raise_notrace Not_hoistable
+  (* Cheap operations. *)
+  | `uop (_, #Insn.copy, _)
+  | `bop (_, #Insn.arith_binop, _, _)
+  | `bop (_, #Insn.bitwise_binop, _, _)
+  | `bop (_, #Insn.cmp, _, _)
+  | `uop (_, #Insn.arith_unop, _)
+  | `uop (_, #Insn.bitwise_unop, _)
+    -> 1
+  (* Moderate operations. *)
+  | `uop (_, #Insn.cast, _)
+  | `sel _
+    -> 2
+
+let blk_cost b =
+  Blk.insns b |> Seq.map ~f:Insn.op |>
+  Seq.sum (module Int) ~f:insn_cost
+
+let max_join_args = 2
+let max_pred_cost = 4
+
+let check_args tenv env fn b =
+  let args = Seq.to_list @@ Blk.args b in
+  List.length args <= max_join_args && try
+    List.iter args ~f:(fun x ->
+        ignore @@ BR.basicty tenv env fn x);
+    true
+  with BR.Non_basic -> false
+
+let (.?[]) env l = Hashtbl.find env.blks l
+let (.![]) env l = Hashtbl.find_exn env.blks l
+
+let check_blk env l j = match env.?[l] with
+  | None -> false
+  | Some b ->
+    try match Blk.ctrl b with
+      | `jmp `label (l', args) when Label.(l' = j) ->
+        (* Ensure that this block has no parameters.
+           We have an invariant that, in its canonical
+           form, the only time a block can have parameters
+           is if it exists as a join point. *)
+        Seq.is_empty (Blk.args b) &&
+        (* Ensure correct arity *)
+        Seq.length (Blk.args env.![j]) = List.length args &&
+        (* Ensure that the block isn't too expensive to copy
+           to the header. *)
+        blk_cost b <= max_pred_cost
+      | _ -> false
+    with Not_hoistable -> false
+
+let check_hdr env l s1 s2 = match env.?[l] with
+  | None -> false
+  | Some b -> match Blk.ctrl b with
+    | `br (_, `label (l1, _), `label (l2, _)) ->
+      Label.((l1 = s1 && l2 = s2) || (l1 = s2 && l2 = s1))
+    | _ -> false
+
+let plist env l = Seq.to_list @@ Cfg.Node.preds l env.cfg
+
+let find_join tenv env fn =
+  with_return @@ fun {return} ->
+  Hashtbl.iteri env.blks ~f:(fun ~key ~data:b ->
+      let found j = return @@ Some (key, j) in
+      if check_args tenv env fn b then match plist env key with
+        | [p1; p2] when Label.(p1 <> p2) ->
+          begin match plist env p1, plist env p2 with
+            | [p1'], _ when Label.(p1' = p2) ->
+              if check_blk env p1 key
+              && check_hdr env p2 p1 key
+              then found @@ triangle p1 p2
+            | _, [p2'] when Label.(p2' = p1) ->
+              if check_blk env p2 key
+              && check_hdr env p1 p2 key
+              then found @@ triangle p2 p1
+            | [p1'], [p2'] when Label.(p1' = p2') ->
+              if check_blk env p1 key
+              && check_blk env p2 key
+              && check_hdr env p1' p1 p2
+              then found @@ diamond p1 p2 p1'
+            | _ -> ()
+          end
+        | _ -> ());
+  None
+
+let canonicalize_diamond env p1 p2 hdr =
+  let b1 = env.![p1] and b2 = env.![p2] and h = env.![hdr] in
+  let ctrl = match Blk.(ctrl h, ctrl b1, ctrl b2) with
+    | `br (c, `label (l1, _), `label (l2, _)),
+      `jmp (`label _ as d1),
+      `jmp (`label _ as d2) ->
+      if Label.(l1 = p1 && l2 = p2) then
+        `br (c, d1, d2)
+      else if Label.(l1 = p2 && l2 = p1) then
+        `br (c, d2, d1)
+      else assert false
+    | _ -> assert false in
+  let i1 = Seq.append (Blk.insns b1) (Blk.insns b2) in
+  let h' = Blk.append_insns h @@ Seq.to_list i1 in
+  let h' = Blk.with_ctrl h' ctrl in
+  Hashtbl.set env.blks ~key:hdr ~data:h'
+
+let canonicalize_triangle env key pred hdr =
+  let b = env.![pred] and h = env.![hdr] in
+  let ctrl = match Blk.(ctrl h, ctrl b) with
+    | `br (c, `label (l1, a1), `label (l2, a2)),
+      `jmp (`label _ as d) ->
+      if Label.(key = l1 && pred = l2) then
+        `br (c, `label (l1, a1), d)
+      else if Label.(key = l2 && pred = l1) then
+        `br (c, d, `label (l2, a2))
+      else assert false
+    | _ -> assert false in
+  let h' = Blk.append_insns h @@ Seq.to_list @@ Blk.insns b in
+  let h' = Blk.with_ctrl h' ctrl in
+  Hashtbl.set env.blks ~key:hdr ~data:h'
+
+let canonicalize env key = function
+  | Diamond {pred1; pred2; hdr} -> canonicalize_diamond env pred1 pred2 hdr
+  | Triangle {pred; hdr} -> canonicalize_triangle env key pred hdr
+
+let run tenv env fn = match find_join tenv env fn with
+  | None -> false
+  | Some (key, data) ->
+    canonicalize env key data;
+    Logs.debug (fun m ->
+        m "%s: join in $%s at %a: %a%!"
+          __FUNCTION__ (Func.name fn)
+          Label.pp key pp_join data);
+    true
diff --git a/src/test/data/opt/and_test.vir.opt b/src/test/data/opt/and_test.vir.opt
index 29a7af3b..34f715ea 100644
--- a/src/test/data/opt/and_test.vir.opt
+++ b/src/test/data/opt/and_test.vir.opt
@@ -2,45 +2,40 @@ module and_test
 
 export function w $foo(w %x, w %y) {
 @2:
-  %0 = and.w %x, 0x3_w ; @29
-  %1 = eq.w %0, 0x0_w ; @30
-  %11 = sel.w %1, %y, %x ; @40
-  ret %11
+  %2 = and.w %x, 0x3_w ; @31
+  %3 = eq.w %2, 0x0_w ; @32
+  %4 = sel.w %3, %y, %x ; @33
+  ret %4
 }
 
 export function w $bar(w %x, w %y) {
 @10:
-  %2 = and.w %x, 0x3_w ; @31
-  %3 = eq.w %2, 0x0_w ; @32
-  br %3, @11, @12
-@11:
-  %4 = add.w %y, 0x1_w ; @33
-  jmp @15(%4)
-@12:
-  %5 = add.w %x, 0x1_w ; @34
-  jmp @15(%5)
-@15(%r.1):
-  ret %r.1
+  %5 = and.w %x, 0x3_w ; @34
+  %6 = eq.w %5, 0x0_w ; @35
+  %7 = add.w %y, 0x1_w ; @36
+  %8 = add.w %x, 0x1_w ; @37
+  %9 = sel.w %6, %7, %8 ; @38
+  ret %9
 }
 
 export function l $baz(l %x) {
 @18:
-  %6 = and.l %x, 0x3_l ; @35
-  switch.l %6, @19 [0x1_l -> @20,
-                    0x2_l -> @21,
-                    0x3_l -> @22]
+  %10 = and.l %x, 0x3_l ; @39
+  switch.l %10, @19 [0x1_l -> @20,
+                     0x2_l -> @21,
+                     0x3_l -> @22]
 @19:
-  %7 = add.l %x, 0x1_l ; @36
-  jmp @24(%7)
+  %11 = add.l %x, 0x1_l ; @40
+  jmp @24(%11)
 @20:
-  %8 = add.l %x, 0x2_l ; @37
-  jmp @24(%8)
+  %12 = add.l %x, 0x2_l ; @41
+  jmp @24(%12)
 @21:
-  %9 = add.l %x, 0x3_l ; @38
-  jmp @24(%9)
+  %13 = add.l %x, 0x3_l ; @42
+  jmp @24(%13)
 @22:
-  %10 = add.l %x, 0x4_l ; @39
-  jmp @24(%10)
+  %14 = add.l %x, 0x4_l ; @43
+  jmp @24(%14)
 @24(%r.1):
   ret %r.1
 }
diff --git a/src/test/data/opt/and_test.vir.opt.sysv.amd64.regalloc b/src/test/data/opt/and_test.vir.opt.sysv.amd64.regalloc
index db19282c..488618c3 100644
--- a/src/test/data/opt/and_test.vir.opt.sysv.amd64.regalloc
+++ b/src/test/data/opt/and_test.vir.opt.sysv.amd64.regalloc
@@ -2,50 +2,48 @@ module and_test
 
 export function $foo { ; returns: rax
 @2:
-  mov eax, edi ; @48
-  and eax, 0x3_w ; @49
-  cmove edi, esi ; @44
-  mov eax, edi ; @41
-  ret ; @42
+  mov eax, edi ; @51
+  and eax, 0x3_w ; @52
+  cmove edi, esi ; @47
+  mov eax, edi ; @44
+  ret ; @45
 }
 
 export function $bar { ; returns: rax
 @10:
-  test edi, 0x3_w ; @56
-  je @11 ; @57
-@12:
-  lea eax, qword ptr [rdi + 0x1] ; @34
-  jmp @15 ; @55
-@11:
-  lea eax, qword ptr [rsi + 0x1] ; @33
-@15:
-  ret ; @51
+  mov ecx, edi ; @60
+  and ecx, 0x3_w ; @61
+  lea edx, qword ptr [rsi + 0x1] ; @36
+  lea eax, qword ptr [rdi + 0x1] ; @37
+  cmp ecx, 0x0_w ; @55
+  cmove eax, edx ; @56
+  ret ; @54
 }
 
 export function $baz { ; returns: rax
 @18:
-  mov rax, rdi ; @86
-  and rax, 0x3_l ; @87
-  je @19 ; @76
-  dec rax ; @78
-  cmp rax, 0x2_l ; @79
-  ja @19 ; @80
-  lea rcx, qword ptr [rip + @74] ; @81
-  movsxd rax, dword ptr [rcx + rax*4] ; @82
-  add rax, rcx ; @83
-  jmp rax ; @84
-  .tbl @74 [@20, @21, @22] ; @85
+  mov rax, rdi ; @84
+  and rax, 0x3_l ; @85
+  je @19 ; @74
+  dec rax ; @76
+  cmp rax, 0x2_l ; @77
+  ja @19 ; @78
+  lea rcx, qword ptr [rip + @72] ; @79
+  movsxd rax, dword ptr [rcx + rax*4] ; @80
+  add rax, rcx ; @81
+  jmp rax ; @82
+  .tbl @72 [@20, @21, @22] ; @83
 @22:
-  lea rax, qword ptr [rdi + 0x4] ; @39
-  jmp @24 ; @73
-@21:
-  lea rax, qword ptr [rdi + 0x3] ; @38
+  lea rax, qword ptr [rdi + 0x4] ; @43
   jmp @24 ; @71
-@20:
-  lea rax, qword ptr [rdi + 0x2] ; @37
+@21:
+  lea rax, qword ptr [rdi + 0x3] ; @42
   jmp @24 ; @69
+@20:
+  lea rax, qword ptr [rdi + 0x2] ; @41
+  jmp @24 ; @67
 @19:
-  lea rax, qword ptr [rdi + 0x1] ; @36
+  lea rax, qword ptr [rdi + 0x1] ; @40
 @24:
-  ret ; @65
+  ret ; @63
 }
diff --git a/src/test/data/opt/branchless.vir.opt b/src/test/data/opt/branchless.vir.opt
index a7a6d766..bf48e885 100644
--- a/src/test/data/opt/branchless.vir.opt
+++ b/src/test/data/opt/branchless.vir.opt
@@ -2,7 +2,7 @@ module foo
 
 export function w $foo(w %x, w %y, w %z) {
 @2:
-  %0 = ne.w %x, 0x0_w ; @15
-  %1 = sel.w %0, %y, %z ; @16
-  ret %1
+  %2 = ne.w %x, 0x0_w ; @17
+  %3 = sel.w %2, %y, %z ; @18
+  ret %3
 }
diff --git a/src/test/data/opt/collatz.vir.opt b/src/test/data/opt/collatz.vir.opt
index 0d30d4d2..df7a2132 100644
--- a/src/test/data/opt/collatz.vir.opt
+++ b/src/test/data/opt/collatz.vir.opt
@@ -4,23 +4,18 @@ export function w $foo(w %n) {
 @2:
   jmp @3(%n, 0x0_w)
 @3(%x.2, %count.2):
-  %0 = gt.w %x.2, 0x1_w ; @27
-  br %0, @6, @7
+  %1 = gt.w %x.2, 0x1_w ; @28
+  br %1, @6, @7
 @6:
-  %1 = and.w %x.2, 0x1_w ; @28
-  %2 = eq.w %1, 0x0_w ; @29
-  br %2, @10, @11
-@10:
+  %2 = and.w %x.2, 0x1_w ; @29
+  %3 = eq.w %2, 0x0_w ; @30
   %4 = lsr.w %x.2, 0x1_w ; @31
-  jmp @15(%4)
-@11:
   %5 = lsl.w %x.2, 0x1_w ; @32
   %6 = add.w %5, %x.2 ; @33
   %7 = add.w %6, 0x1_w ; @34
-  jmp @15(%7)
-@15(%x.3):
-  %3 = add.w %count.2, 0x1_w ; @30
-  jmp @3(%x.3, %3)
+  %8 = sel.w %3, %4, %7 ; @35
+  %9 = add.w %count.2, 0x1_w ; @36
+  jmp @3(%8, %9)
 @7:
   ret %count.2
 }
diff --git a/src/test/data/opt/collatz.vir.opt.sir b/src/test/data/opt/collatz.vir.opt.sir
index 5bbdd8f2..491c3182 100644
--- a/src/test/data/opt/collatz.vir.opt.sir
+++ b/src/test/data/opt/collatz.vir.opt.sir
@@ -5,19 +5,16 @@ start:
   %x.2 = copy.w %n;
   %count.2 = copy.w 0x0_w;
   while gt.w %x.2, 0x1_w {
-    %1 = and.w %x.2, 0x1_w;
-    if eq.w %1, 0x0_w {
-      %4 = lsr.w %x.2, 0x1_w;
-      %x.3 = copy.w %4
-    } else {
-      %5 = lsl.w %x.2, 0x1_w;
-      %6 = add.w %5, %x.2;
-      %7 = add.w %6, 0x1_w;
-      %x.3 = copy.w %7
-    };
-    %3 = add.w %count.2, 0x1_w;
-    %x.2 = copy.w %x.3;
-    %count.2 = copy.w %3
+    %2 = and.w %x.2, 0x1_w;
+    %3 = eq.w %2, 0x0_w;
+    %4 = lsr.w %x.2, 0x1_w;
+    %5 = lsl.w %x.2, 0x1_w;
+    %6 = add.w %5, %x.2;
+    %7 = add.w %6, 0x1_w;
+    %8 = sel.w %3, %4, %7;
+    %9 = add.w %count.2, 0x1_w;
+    %x.2 = copy.w %8;
+    %count.2 = copy.w %9
   };
   ret %count.2
 }
diff --git a/src/test/data/opt/collatz.vir.opt.sysv b/src/test/data/opt/collatz.vir.opt.sysv
index fd38f3a8..cc94b534 100644
--- a/src/test/data/opt/collatz.vir.opt.sysv
+++ b/src/test/data/opt/collatz.vir.opt.sysv
@@ -4,23 +4,18 @@ export function $foo(w %n/rdi) {
 @2:
   jmp @3(%n, 0x0_w)
 @3(%x.2, %count.2):
-  %0 = gt.w %x.2, 0x1_w ; @27
-  br %0, @6, @7
+  %1 = gt.w %x.2, 0x1_w ; @28
+  br %1, @6, @7
 @6:
-  %1 = and.w %x.2, 0x1_w ; @28
-  %2 = eq.w %1, 0x0_w ; @29
-  br %2, @10, @11
-@10:
+  %2 = and.w %x.2, 0x1_w ; @29
+  %3 = eq.w %2, 0x0_w ; @30
   %4 = lsr.w %x.2, 0x1_w ; @31
-  jmp @15(%4)
-@11:
   %5 = lsl.w %x.2, 0x1_w ; @32
   %6 = add.w %5, %x.2 ; @33
   %7 = add.w %6, 0x1_w ; @34
-  jmp @15(%7)
-@15(%x.3):
-  %3 = add.w %count.2, 0x1_w ; @30
-  jmp @3(%x.3, %3)
+  %8 = sel.w %3, %4, %7 ; @35
+  %9 = add.w %count.2, 0x1_w ; @36
+  jmp @3(%8, %9)
 @7:
   ret rax/%count.2
 }
diff --git a/src/test/data/opt/collatz.vir.opt.sysv.amd64 b/src/test/data/opt/collatz.vir.opt.sysv.amd64
index f651c79e..4bc3dcd5 100644
--- a/src/test/data/opt/collatz.vir.opt.sysv.amd64
+++ b/src/test/data/opt/collatz.vir.opt.sysv.amd64
@@ -2,33 +2,28 @@ module foo
 
 export function $foo { ; returns: rax
 @2:
-  mov %n:w, edi ; @56
-  mov %x.2:w, %n:w ; @57
-  xor %count.2:w, %count.2:w ; @58
-  jmp @3 ; @59
+  mov %n:w, edi ; @53
+  mov %x.2:w, %n:w ; @54
+  xor %count.2:w, %count.2:w ; @55
+  jmp @3 ; @56
 @3:
-  cmp %x.2:w, 0x1_w ; @51
-  ja @6 ; @52
-  jmp @7 ; @53
+  cmp %x.2:w, 0x1_w ; @48
+  ja @6 ; @49
+  jmp @7 ; @50
 @7:
-  mov eax, %count.2:w ; @49
-  ret ; @50
+  mov eax, %count.2:w ; @46
+  ret ; @47
 @6:
-  test %x.2:w, 0x1_w ; @43
-  je @10 ; @44
-  jmp @11 ; @45
-@11:
-  lea %7:w, qword ptr [%x.2 + %x.2*2 + 0x1] ; @34
-  mov %x.3:w, %7:w ; @41
-  jmp @15 ; @42
-@10:
+  mov %2:w, %x.2:w ; @29
+  and %2:w, 0x1_w ; @45
   mov %4:w, %x.2:w ; @31
-  shr %4:w, 0x1_b ; @40
-  mov %x.3:w, %4:w ; @38
-  jmp @15 ; @39
-@15:
-  lea %3:w, qword ptr [%count.2 + 0x1] ; @30
-  mov %x.2:w, %x.3:w ; @35
-  mov %count.2:w, %3:w ; @36
-  jmp @3 ; @37
+  shr %4:w, 0x1_b ; @42
+  lea %7:w, qword ptr [%x.2 + %x.2*2 + 0x1] ; @34
+  mov %8:w, %7:w ; @35
+  cmp %2:w, 0x0_w ; @40
+  cmove %8:w, %4:w ; @41
+  lea %9:w, qword ptr [%count.2 + 0x1] ; @36
+  mov %x.2:w, %8:w ; @37
+  mov %count.2:w, %9:w ; @38
+  jmp @3 ; @39
 }
diff --git a/src/test/data/opt/collatz.vir.opt.sysv.amd64.regalloc b/src/test/data/opt/collatz.vir.opt.sysv.amd64.regalloc
index a0cd04de..788c2a34 100644
--- a/src/test/data/opt/collatz.vir.opt.sysv.amd64.regalloc
+++ b/src/test/data/opt/collatz.vir.opt.sysv.amd64.regalloc
@@ -2,21 +2,20 @@ module foo
 
 export function $foo { ; returns: rax
 @2:
-  xor eax, eax ; @58
+  xor eax, eax ; @55
 @3:
-  cmp edi, 0x1_w ; @51
-  ja @6 ; @52
+  cmp edi, 0x1_w ; @48
+  ja @6 ; @49
 @7:
-  ret ; @50
+  ret ; @47
 @6:
-  test edi, 0x1_w ; @43
-  je @10 ; @44
-@11:
+  mov edx, edi ; @29
+  and edx, 0x1_w ; @45
+  mov ecx, edi ; @31
+  shr ecx, 0x1_b ; @42
   lea edi, qword ptr [rdi + rdi*2 + 0x1] ; @34
-  jmp @15 ; @42
-@10:
-  shr edi, 0x1_b ; @40
-@15:
-  inc eax ; @30
-  jmp @3 ; @37
+  cmp edx, 0x0_w ; @40
+  cmove edi, ecx ; @41
+  inc eax ; @36
+  jmp @3 ; @39
 }
diff --git a/src/test/data/opt/contractsel.vir.opt b/src/test/data/opt/contractsel.vir.opt
index 48755380..f5a98f58 100644
--- a/src/test/data/opt/contractsel.vir.opt
+++ b/src/test/data/opt/contractsel.vir.opt
@@ -3,11 +3,8 @@ module foo
 function w $foo(w %x) {
 @2:
   %0 = sgt.w %x, 0x2a_w ; @14
-  br %0, @6(0x5_w), @4
-@4:
   %1 = slt.w %x, 0x0_w ; @15
   %2 = sel.w %1, 0x3_w, %x ; @16
-  jmp @6(%2)
-@6(%y.1):
-  ret %y.1
+  %3 = sel.w %0, 0x5_w, %2 ; @17
+  ret %3
 }
diff --git a/src/test/data/opt/contractsel.vir.opt.sysv.amd64 b/src/test/data/opt/contractsel.vir.opt.sysv.amd64
index fed727aa..4d338f6f 100644
--- a/src/test/data/opt/contractsel.vir.opt.sysv.amd64
+++ b/src/test/data/opt/contractsel.vir.opt.sysv.amd64
@@ -3,19 +3,12 @@ module foo
 function $foo { ; returns: rax
 @2:
   mov %x:w, edi ; @14
-  cmp %x:w, 0x2a_w ; @28
-  jg @17 ; @29
-  jmp @4 ; @30
-@17:
-  mov %y.1:w, 0x5_w ; @26
-  jmp @6 ; @27
-@4:
   mov %2:w, 0x3_w ; @16
   cmp %x:w, 0x0_w ; @22
   cmovge %2:w, %x:w ; @23
-  mov %y.1:w, %2:w ; @20
-  jmp @6 ; @21
-@6:
-  mov eax, %y.1:w ; @18
+  mov %3:w, 0x5_w ; @17
+  cmp %x:w, 0x2a_w ; @20
+  cmovle %3:w, %2:w ; @21
+  mov eax, %3:w ; @18
   ret ; @19
 }
diff --git a/src/test/data/opt/contractsel.vir.opt.sysv.amd64.regalloc b/src/test/data/opt/contractsel.vir.opt.sysv.amd64.regalloc
index 92b029f2..356588fd 100644
--- a/src/test/data/opt/contractsel.vir.opt.sysv.amd64.regalloc
+++ b/src/test/data/opt/contractsel.vir.opt.sysv.amd64.regalloc
@@ -2,15 +2,11 @@ module foo
 
 function $foo { ; returns: rax
 @2:
-  cmp edi, 0x2a_w ; @28
-  jle @4 ; @29
-@17:
-  mov eax, 0x5_w ; @26
-  jmp @6 ; @27
-@4:
-  mov eax, 0x3_w ; @16
+  mov ecx, 0x3_w ; @16
   cmp edi, 0x0_w ; @22
-  cmovge eax, edi ; @23
-@6:
+  cmovge ecx, edi ; @23
+  mov eax, 0x5_w ; @17
+  cmp edi, 0x2a_w ; @20
+  cmovle eax, ecx ; @21
   ret ; @19
 }
diff --git a/src/test/data/opt/csehoistandmerge2.vir.opt b/src/test/data/opt/csehoistandmerge2.vir.opt
index 3e46773d..1c922dce 100644
--- a/src/test/data/opt/csehoistandmerge2.vir.opt
+++ b/src/test/data/opt/csehoistandmerge2.vir.opt
@@ -2,9 +2,9 @@ module foo
 
 export function w $foo(w %x, w %y) {
 @2:
-  %0 = slt.w %y, 0x0_w ; @11
-  %1 = add.w %x, 0x1_w ; @12
-  %3 = sel.w %0, %1, 0x5_w ; @14
-  %2 = add.w %3, %1 ; @13
-  ret %2
+  %1 = slt.w %y, 0x0_w ; @12
+  %2 = add.w %x, 0x1_w ; @13
+  %3 = sel.w %1, %2, 0x5_w ; @14
+  %4 = add.w %3, %2 ; @15
+  ret %4
 }
diff --git a/src/test/data/opt/csehoistandmerge3.vir.opt b/src/test/data/opt/csehoistandmerge3.vir.opt
index 79de6569..5b54e671 100644
--- a/src/test/data/opt/csehoistandmerge3.vir.opt
+++ b/src/test/data/opt/csehoistandmerge3.vir.opt
@@ -2,13 +2,10 @@ module foo
 
 export function w $foo(w %x, w %y) {
 @2:
-  %0 = slt.w %y, 0x0_w ; @11
-  %1 = add.w %x, 0x1_w ; @12
-  br %0, @6(%1), @4
-@4:
+  %1 = slt.w %y, 0x0_w ; @12
+  %2 = add.w %x, 0x1_w ; @13
   %3 = sub.w %x, 0x1_w ; @14
-  jmp @6(%3)
-@6(%a.1):
-  %2 = add.w %a.1, %1 ; @13
-  ret %2
+  %4 = sel.w %1, %2, %3 ; @15
+  %5 = add.w %4, %2 ; @16
+  ret %5
 }
diff --git a/src/test/data/opt/csehoistandmergecommute.vir.opt b/src/test/data/opt/csehoistandmergecommute.vir.opt
index 9a98d14e..d8aa7d99 100644
--- a/src/test/data/opt/csehoistandmergecommute.vir.opt
+++ b/src/test/data/opt/csehoistandmergecommute.vir.opt
@@ -2,6 +2,6 @@ module foo
 
 export function w $foo(w %x, w %y) {
 @2:
-  %1 = add.w %y, %x ; @10
-  ret %1
+  %2 = add.w %x, %y ; @11
+  ret %2
 }
diff --git a/src/test/data/opt/esc1.vir.opt b/src/test/data/opt/esc1.vir.opt
index 6d33a0e6..a4781860 100644
--- a/src/test/data/opt/esc1.vir.opt
+++ b/src/test/data/opt/esc1.vir.opt
@@ -4,17 +4,17 @@ export function w $foo(w %x) {
   %a = slot 8, align 8
   %b = slot 8, align 8
 @2:
-  %0 = add.w %x, 0x1_w ; @19
-  %1 = add.w %x, 0x2_w ; @20
-  %2 = add.w %x, 0x3_w ; @21
+  %1 = add.w %x, 0x1_w ; @20
+  %2 = add.w %x, 0x2_w ; @21
+  %3 = add.w %x, 0x3_w ; @22
   st.w %x, %a ; @8
-  %3 = add.l %a, 0x4_l ; @22
-  st.w %0, %3 ; @10
-  st.w %1, %b ; @11
-  %4 = add.l %b, 0x4_l ; @23
-  st.w %2, %4 ; @13
-  %5 = slt.w %x, 0x0_w ; @24
-  %6 = sel.l %5, %4, %3 ; @25
-  %r.1 = ld.w %6 ; @18
+  %4 = add.l %a, 0x4_l ; @23
+  st.w %1, %4 ; @10
+  st.w %2, %b ; @11
+  %5 = add.l %b, 0x4_l ; @24
+  st.w %3, %5 ; @13
+  %6 = slt.w %x, 0x0_w ; @25
+  %7 = sel.l %6, %5, %4 ; @26
+  %r.1 = ld.w %7 ; @18
   ret %r.1
 }
diff --git a/src/test/data/opt/evenodd.vir.opt b/src/test/data/opt/evenodd.vir.opt
index 20bdda3a..c824fcdf 100644
--- a/src/test/data/opt/evenodd.vir.opt
+++ b/src/test/data/opt/evenodd.vir.opt
@@ -2,37 +2,34 @@ module evenodd
 
 function w $abs(w %n) {
 @2:
-  %3 = slt.w %n, 0x0_w ; @24
-  br %3, @3, @21(%n)
-@3:
-  %4 = neg.w %n ; @25
-  jmp @21(%4)
-@21(%0):
-  ret %0
+  %4 = slt.w %n, 0x0_w ; @25
+  %5 = neg.w %n ; @26
+  %6 = sel.w %4, %5, %n ; @27
+  ret %6
 }
 
 export function b $even(w %n) {
 @7:
   %n.1 = call.w $abs(%n) ; @10
-  %5 = eq.w %n.1, 0x0_w ; @26
-  br %5, @22(0x1_b), @9
+  %7 = eq.w %n.1, 0x0_w ; @28
+  br %7, @23(0x1_b), @9
 @9:
-  %6 = sub.w %n.1, 0x1_w ; @27
-  %b.1 = call.b $odd(%6) ; @13
-  jmp @22(%b.1)
-@22(%1):
-  ret %1
+  %8 = sub.w %n.1, 0x1_w ; @29
+  %b.1 = call.b $odd(%8) ; @13
+  jmp @23(%b.1)
+@23(%2):
+  ret %2
 }
 
 export function b $odd(w %n) {
 @14:
   %n.1 = call.w $abs(%n) ; @17
-  %7 = eq.w %n.1, 0x0_w ; @28
-  br %7, @23(0x0_b), @16
+  %9 = eq.w %n.1, 0x0_w ; @30
+  br %9, @24(0x0_b), @16
 @16:
-  %8 = sub.w %n.1, 0x1_w ; @29
-  %b.1 = call.b $even(%8) ; @20
-  jmp @23(%b.1)
-@23(%2):
-  ret %2
+  %10 = sub.w %n.1, 0x1_w ; @31
+  %b.1 = call.b $even(%10) ; @20
+  jmp @24(%b.1)
+@24(%3):
+  ret %3
 }
diff --git a/src/test/data/opt/evenodd.vir.opt.sysv b/src/test/data/opt/evenodd.vir.opt.sysv
index cb1d7432..16d865e5 100644
--- a/src/test/data/opt/evenodd.vir.opt.sysv
+++ b/src/test/data/opt/evenodd.vir.opt.sysv
@@ -2,37 +2,34 @@ module evenodd
 
 function $abs(w %n/rdi) {
 @2:
-  %3 = slt.w %n, 0x0_w ; @24
-  br %3, @3, @21(%n)
-@3:
-  %4 = neg.w %n ; @25
-  jmp @21(%4)
-@21(%0):
-  ret rax/%0
+  %4 = slt.w %n, 0x0_w ; @25
+  %5 = neg.w %n ; @26
+  %6 = sel.w %4, %5, %n ; @27
+  ret rax/%6
 }
 
 export function $even(w %n/rdi) {
 @7:
   %n.1/w/rax = call $abs(%n/rdi) ; @10
-  %5 = eq.w %n.1, 0x0_w ; @26
-  br %5, @22(0x1_b), @9
+  %7 = eq.w %n.1, 0x0_w ; @28
+  br %7, @23(0x1_b), @9
 @9:
-  %6 = sub.w %n.1, 0x1_w ; @27
-  %b.1/b/rax = call $odd(%6/rdi) ; @13
-  jmp @22(%b.1)
-@22(%1):
-  ret rax/%1
+  %8 = sub.w %n.1, 0x1_w ; @29
+  %b.1/b/rax = call $odd(%8/rdi) ; @13
+  jmp @23(%b.1)
+@23(%2):
+  ret rax/%2
 }
 
 export function $odd(w %n/rdi) {
 @14:
   %n.1/w/rax = call $abs(%n/rdi) ; @17
-  %7 = eq.w %n.1, 0x0_w ; @28
-  br %7, @23(0x0_b), @16
+  %9 = eq.w %n.1, 0x0_w ; @30
+  br %9, @24(0x0_b), @16
 @16:
-  %8 = sub.w %n.1, 0x1_w ; @29
-  %b.1/b/rax = call $even(%8/rdi) ; @20
-  jmp @23(%b.1)
-@23(%2):
-  ret rax/%2
+  %10 = sub.w %n.1, 0x1_w ; @31
+  %b.1/b/rax = call $even(%10/rdi) ; @20
+  jmp @24(%b.1)
+@24(%3):
+  ret rax/%3
 }
diff --git a/src/test/data/opt/evenodd.vir.opt.sysv.amd64 b/src/test/data/opt/evenodd.vir.opt.sysv.amd64
index b095ecec..545b965b 100644
--- a/src/test/data/opt/evenodd.vir.opt.sysv.amd64
+++ b/src/test/data/opt/evenodd.vir.opt.sysv.amd64
@@ -2,67 +2,60 @@ module evenodd
 
 function $abs { ; returns: rax
 @2:
-  mov %n:w, edi ; @24
-  test %n:w, %n:w ; @38
-  js @3 ; @39
-  jmp @30 ; @40
-@30:
-  mov %0:w, %n:w ; @36
-  jmp @21 ; @37
-@3:
-  mov %4:w, %n:w ; @25
-  neg %4:w ; @35
-  mov %0:w, %4:w ; @33
-  jmp @21 ; @34
-@21:
-  mov eax, %0:w ; @31
-  ret ; @32
+  mov %n:w, edi ; @25
+  mov %5:w, %n:w ; @26
+  neg %5:w ; @36
+  mov %6:w, %n:w ; @27
+  cmp %n:w, 0x0_w ; @34
+  cmovl %6:w, %5:w ; @35
+  mov eax, %6:w ; @32
+  ret ; @33
 }
 
 export function $even { ; returns: rax
 @7:
   mov %n:w, edi ; @10
-  mov edi, %n:w ; @58
-  call $abs ; rdi ; @59
-  mov %n.1:w, eax ; @60
-  test %n.1:w, %n.1:w ; @53
-  je @44 ; @54
-  jmp @9 ; @55
-@44:
-  mov %1:b, 0x1_b ; @51
-  jmp @22 ; @52
+  mov edi, %n:w ; @54
+  call $abs ; rdi ; @55
+  mov %n.1:w, eax ; @56
+  test %n.1:w, %n.1:w ; @49
+  je @40 ; @50
+  jmp @9 ; @51
+@40:
+  mov %2:b, 0x1_b ; @47
+  jmp @23 ; @48
 @9:
-  lea %6:w, qword ptr [%n.1 - 0x1] ; @27
-  mov edi, %6:w ; @13
-  call $odd ; rdi ; @49
-  mov %b.1:b, al ; @50
-  mov %1:b, %b.1:b ; @47
-  jmp @22 ; @48
-@22:
-  mov al, %1:b ; @45
-  ret ; @46
+  lea %8:w, qword ptr [%n.1 - 0x1] ; @29
+  mov edi, %8:w ; @13
+  call $odd ; rdi ; @45
+  mov %b.1:b, al ; @46
+  mov %2:b, %b.1:b ; @43
+  jmp @23 ; @44
+@23:
+  mov al, %2:b ; @41
+  ret ; @42
 }
 
 export function $odd { ; returns: rax
 @14:
   mov %n:w, edi ; @17
-  mov edi, %n:w ; @75
-  call $abs ; rdi ; @76
-  mov %n.1:w, eax ; @77
-  test %n.1:w, %n.1:w ; @70
-  je @61 ; @71
-  jmp @16 ; @72
-@61:
-  xor %2:b, %2:b ; @68
-  jmp @23 ; @69
+  mov edi, %n:w ; @71
+  call $abs ; rdi ; @72
+  mov %n.1:w, eax ; @73
+  test %n.1:w, %n.1:w ; @66
+  je @57 ; @67
+  jmp @16 ; @68
+@57:
+  xor %3:b, %3:b ; @64
+  jmp @24 ; @65
 @16:
-  lea %8:w, qword ptr [%n.1 - 0x1] ; @29
-  mov edi, %8:w ; @20
-  call $even ; rdi ; @66
-  mov %b.1:b, al ; @67
-  mov %2:b, %b.1:b ; @64
-  jmp @23 ; @65
-@23:
-  mov al, %2:b ; @62
-  ret ; @63
+  lea %10:w, qword ptr [%n.1 - 0x1] ; @31
+  mov edi, %10:w ; @20
+  call $even ; rdi ; @62
+  mov %b.1:b, al ; @63
+  mov %3:b, %b.1:b ; @60
+  jmp @24 ; @61
+@24:
+  mov al, %3:b ; @58
+  ret ; @59
 }
diff --git a/src/test/data/opt/evenodd.vir.opt.sysv.amd64.regalloc b/src/test/data/opt/evenodd.vir.opt.sysv.amd64.regalloc
index 503dbb1e..405c2107 100644
--- a/src/test/data/opt/evenodd.vir.opt.sysv.amd64.regalloc
+++ b/src/test/data/opt/evenodd.vir.opt.sysv.amd64.regalloc
@@ -2,47 +2,46 @@ module evenodd
 
 function $abs { ; returns: rax
 @2:
-  test edi, edi ; @38
-  jns @21 ; @39
-@3:
-  neg edi ; @35
-@21:
-  mov eax, edi ; @31
-  ret ; @32
+  mov eax, edi ; @26
+  neg eax ; @36
+  cmp edi, 0x0_w ; @34
+  cmovl edi, eax ; @35
+  mov eax, edi ; @32
+  ret ; @33
 }
 
 export function $even { ; returns: rax
 @7:
-  push rbp ; @78
-  mov rbp, rsp ; @79
-  call $abs ; rdi ; @59
-  test eax, eax ; @53
-  jne @9 ; @54
-@44:
-  mov al, 0x1_b ; @51
-  jmp @22 ; @52
+  push rbp ; @74
+  mov rbp, rsp ; @75
+  call $abs ; rdi ; @55
+  test eax, eax ; @49
+  jne @9 ; @50
+@40:
+  mov al, 0x1_b ; @47
+  jmp @23 ; @48
 @9:
-  lea edi, qword ptr [rax - 0x1] ; @27
-  call $odd ; rdi ; @49
-@22:
-  leave ; @80
-  ret ; @46
+  lea edi, qword ptr [rax - 0x1] ; @29
+  call $odd ; rdi ; @45
+@23:
+  leave ; @76
+  ret ; @42
 }
 
 export function $odd { ; returns: rax
 @14:
-  push rbp ; @81
-  mov rbp, rsp ; @82
-  call $abs ; rdi ; @76
-  test eax, eax ; @70
-  jne @16 ; @71
-@61:
-  xor al, al ; @68
-  jmp @23 ; @69
+  push rbp ; @77
+  mov rbp, rsp ; @78
+  call $abs ; rdi ; @72
+  test eax, eax ; @66
+  jne @16 ; @67
+@57:
+  xor al, al ; @64
+  jmp @24 ; @65
 @16:
-  lea edi, qword ptr [rax - 0x1] ; @29
-  call $even ; rdi ; @66
-@23:
-  leave ; @83
-  ret ; @63
+  lea edi, qword ptr [rax - 0x1] ; @31
+  call $even ; rdi ; @62
+@24:
+  leave ; @79
+  ret ; @59
 }
diff --git a/src/test/data/opt/ifc1.vir b/src/test/data/opt/ifc1.vir
new file mode 100644
index 00000000..c2a54be6
--- /dev/null
+++ b/src/test/data/opt/ifc1.vir
@@ -0,0 +1,202 @@
+module ifc1
+
+;; a simple diamond where both blocks are cheap
+export function w $simple_diamond(w %x) {
+@start:
+  %c = slt.w %x, 0_w
+  br %c, @neg, @pos
+@neg:
+  %y = add.w %x, 5_w
+  jmp @join
+@pos:
+  %y = sub.w %x, 5_w
+  jmp @join
+@join:
+  ret %y
+}
+
+;; simple triangle
+export function w $right_triangle(w %x) {
+@start:
+  %c = slt.w %x, 0_w
+  br %c, @join, @pos
+@pos:
+  %x = sub.w %x, 5_w
+  jmp @join
+@join:
+  ret %x
+}
+
+;; other case of a simple triangle
+export function w $left_triangle(w %x) {
+@start:
+  %c = slt.w %x, 0_w
+  br %c, @neg, @join
+@neg:
+  %x = add.w %x, 5_w
+  jmp @join
+@join:
+  ret %x
+}
+
+;; diamond where both blocks are too expensive
+export function w $expensive_diamond(w %x) {
+@start:
+  %c = slt.w %x, 0_w
+  br %c, @neg, @pos
+@neg:
+  %y = add.w %x, 5_w
+  %y = mul.w %y, 13_w
+  jmp @join
+@pos:
+  %y = sub.w %x, 5_w
+  %y = div.w %y, 3_w
+  jmp @join
+@join:
+  ret %y
+}
+
+;; diamond with one cheap block and one expensive block
+export function w $mixed_cost(w %x) {
+@start:
+  %c = slt.w %x, 0_w
+  br %c, @cheap, @expensive
+@cheap:
+  %y = add.w %x, 1_w
+  jmp @join
+@expensive:
+  %y = mul.w %x, 97_w
+  %y = div.w %y, 7_w
+  jmp @join
+@join:
+  ret %y
+}
+
+;; TODO: only inner triangle should canonicalize,
+;; but currently @join1 has more than two predecessors
+export function w $nested_tri(w %x) {
+@start:
+  %c1 = slt.w %x, 0_w
+  br %c1, @join1, @mid
+@mid:
+  %c2 = eq.w %x, 10_w
+  br %c2, @join1, @body
+@body:
+  %x = add.w %x, 1_w
+  jmp @join1
+@join1:
+  ret %x
+}
+
+;; back-to-back diamonds: make sure that
+;; the canonicalization happens in the
+;; correct order
+export function w $chain(w %x) {
+@start:
+  %c1 = slt.w %x, 0_w
+  br %c1, @neg1, @pos1
+@neg1:
+  %x = add.w %x, 1_w
+  jmp @mid
+@pos1:
+  %x = sub.w %x, 1_w
+  jmp @mid
+@mid:
+  %c2 = slt.w %x, 10_w
+  br %c2, @neg2, @pos2
+@neg2:
+  %x = add.w %x, 2_w
+  jmp @join
+@pos2:
+  %x = sub.w %x, 2_w
+  jmp @join
+@join:
+  ret %x
+}
+
+;; GVN should collapse %y to %x
+export function w $redundant_phi(w %x) {
+@start:
+  %c = slt.w %x, 0_w
+  br %c, @neg, @pos
+@neg:
+  %y = add.w %x, 0_w
+  jmp @join
+@pos:
+  %y = add.w %x, 0_w
+  jmp @join
+@join:
+  ret %y
+}
+
+;; this should canonicalize to a triangle
+;; before if-conversion happens
+export function w $dead_arm(w %x) {
+@start:
+  %c = slt.w %x, 0_w
+  br %c, @neg, @pos
+@neg:
+  jmp @join
+@pos:
+  %x = add.w %x, 1_w
+  jmp @join
+@join:
+  ret %x
+}
+
+;; TODO: the @loop header has more than two
+;; prececessors, so we don't canonicalize
+export function w $loop_if(w %x) {
+@start:
+  jmp @loop
+@loop:
+  %c1 = slt.w %x, 100_w
+  br %c1, @body, @exit
+@body:
+  %c2 = slt.w %x, 0_w
+  br %c2, @neg, @pos
+@neg:
+  %x = add.w %x, 1_w
+  jmp @join
+@pos:
+  %x = sub.w %x, 1_w
+  jmp @join
+@join:
+  jmp @loop
+@exit:
+  ret %x
+}
+
+;; %y's dominance of %z must be preserved
+export function w $dominance(w %x) {
+@start:
+  %c = slt.w %x, 0_w
+  br %c, @neg, @pos
+@neg:
+  %y = add.w %x, 1_w
+  jmp @join
+@pos:
+  %y = add.w %x, 2_w
+  jmp @join
+@join:
+  %z = mul.w %y, %x
+  ret %z
+}
+
+;; TODO: handle switch?
+export function w $switch_like(w %x) {
+@start:
+  switch.w %x, @dflt [0_w -> @c0,
+                      1_w -> @c1]
+@c0:
+  %y = add.w %x, 1_w
+  jmp @join
+@c1:
+  %y = sub.w %x, 1_w
+  jmp @join
+@dflt:
+  %y = mul.w %x, 2_w
+  jmp @join
+@join:
+  ret %y
+}
diff --git a/src/test/data/opt/ifc1.vir.opt b/src/test/data/opt/ifc1.vir.opt
new file mode 100644
index 00000000..8b30df5e
--- /dev/null
+++ b/src/test/data/opt/ifc1.vir.opt
@@ -0,0 +1,145 @@
+module ifc1
+
+export function w $simple_diamond(w %x) {
+@2:
+  %8 = slt.w %x, 0x0_w ; @104
+  %9 = add.w %x, 0x5_w ; @105
+  %10 = sub.w %x, 0x5_w ; @106
+  %11 = sel.w %8, %9, %10 ; @107
+  ret %11
+}
+
+export function w $right_triangle(w %x) {
+@9:
+  %12 = slt.w %x, 0x0_w ; @108
+  %13 = sub.w %x, 0x5_w ; @109
+  %14 = sel.w %12, %x, %13 ; @110
+  ret %14
+}
+
+export function w $left_triangle(w %x) {
+@14:
+  %15 = slt.w %x, 0x0_w ; @111
+  %16 = add.w %x, 0x5_w ; @112
+  %17 = sel.w %15, %16, %x ; @113
+  ret %17
+}
+
+export function w $expensive_diamond(w %x) {
+@19:
+  %18 = slt.w %x, 0x0_w ; @114
+  br %18, @20, @21
+@20:
+  %19 = add.w %x, 0x5_w ; @115
+  %20 = lsl.w %19, 0x4_w ; @116
+  %21 = lsl.w %19, 0x1_w ; @117
+  %22 = sub.w %20, %21 ; @118
+  %23 = sub.w %22, %19 ; @119
+  jmp @23(%23)
+@21:
+  %25 = sub.w %x, 0x5_w ; @121
+  %26 = mulh.w %25, 0x55555556_w ; @122
+  %27 = lsr.w %26, 0x1f_w ; @123
+  %28 = add.w %26, %27 ; @124
+  jmp @23(%28)
+@23(%y.1):
+  ret %y.1
+}
+
+export function w $mixed_cost(w %x) {
+@28:
+  %29 = slt.w %x, 0x0_w ; @125
+  br %29, @29, @30
+@29:
+  %30 = add.w %x, 0x1_w ; @126
+  jmp @32(%30)
+@30:
+  %31 = lsl.w %x, 0x7_w ; @127
+  %32 = lsl.w %x, 0x5_w ; @128
+  %33 = sub.w %32, %x ; @129
+  %34 = sub.w %31, %33 ; @130
+  %35 = div.w %34, 0x7_w ; @131
+  jmp @32(%35)
+@32(%y.1):
+  ret %y.1
+}
+
+export function w $nested_tri(w %x) {
+@36:
+  %41 = slt.w %x, 0x0_w ; @137
+  br %41, @37(%x), @38
+@38:
+  %42 = eq.w %x, 0xa_w ; @138
+  br %42, @37(%x), @40
+@40:
+  %43 = add.w %x, 0x1_w ; @139
+  jmp @37(%43)
+@37(%x.1):
+  ret %x.1
+}
+
+export function w $chain(w %x) {
+@43:
+  %44 = slt.w %x, 0x0_w ; @140
+  %45 = add.w %x, 0x1_w ; @141
+  %46 = sub.w %x, 0x1_w ; @142
+  %47 = sel.w %44, %45, %46 ; @143
+  %48 = slt.w %47, 0xa_w ; @144
+  %49 = add.w %47, 0x2_w ; @145
+  %50 = sub.w %47, 0x2_w ; @146
+  %51 = sel.w %48, %49, %50 ; @147
+  ret %51
+}
+
+export function w $redundant_phi(w %x) {
+@56:
+  ret %x
+}
+
+export function w $dead_arm(w %x) {
+@63:
+  %53 = slt.w %x, 0x0_w ; @149
+  %54 = add.w %x, 0x1_w ; @150
+  %55 = sel.w %53, %x, %54 ; @151
+  ret %55
+}
+
+export function w $loop_if(w %x) {
+@69:
+  jmp @70(%x)
+@70(%x.1):
+  %56 = slt.w %x.1, 0x64_w ; @152
+  br %56, @71, @72
+@71:
+  %57 = slt.w %x.1, 0x0_w ; @153
+  br %57, @74, @75
+@74:
+  %58 = add.w %x.1, 0x1_w ; @154
+  jmp @70(%58)
+@75:
+  %59 = sub.w %x.1, 0x1_w ; @155
+  jmp @70(%59)
+@72:
+  ret %x.1
+}
+
+export function w $dominance(w %x) {
+@80:
+  %60 = slt.w %x, 0x0_w ; @156
+  %61 = add.w %x, 0x1_w ; @157
+  %62 = add.w %x, 0x2_w ; @158
+  %63 = sel.w %60, %61, %62 ; @159
+  %64 = mul.w %63, %x ; @160
+  ret %64
+}
+
+export function w $switch_like(w %x) {
+@88:
+  switch.w %x, @89 [0x0_w -> @92(0x1_w),
+                    0x1_w -> @92(0x0_w)]
+@89:
+  %65 = lsl.w %x, 0x1_w ; @161
+  jmp @92(%65)
+@92(%y.1):
+  ret %y.1
+}
diff --git a/src/test/data/opt/palindrome.vir.opt b/src/test/data/opt/palindrome.vir.opt
index b2b1df22..3bcc02eb 100644
--- a/src/test/data/opt/palindrome.vir.opt
+++ b/src/test/data/opt/palindrome.vir.opt
@@ -7,18 +7,19 @@ export function b $palindrome(w %n) {
   %0 = ne.w %n.1, 0x0_w ; @15
   br %0, @6, @7
 @6:
-  %1 = mulh.w %n.1, 0x1999999a_w ; @16
-  %2 = lsr.w %1, 0x1f_w ; @17
-  %3 = add.w %1, %2 ; @18
-  %4 = mul.w %3, 0xa_w ; @19
-  %5 = sub.w %n.1, %4 ; @20
-  %11 = lsl.w %rev.2, 0x3_w ; @26
-  %12 = lsl.w %rev.2, 0x1_w ; @27
-  %13 = add.w %11, %12 ; @28
-  %14 = add.w %13, %5 ; @29
-  jmp @3(%14, %3)
+  %1 = mulh.w %n.1, 0x66666667_w ; @16
+  %2 = asr.w %1, 0x2_w ; @17
+  %3 = lsr.w %1, 0x1f_w ; @18
+  %4 = add.w %2, %3 ; @19
+  %5 = mul.w %4, 0xa_w ; @20
+  %6 = sub.w %n.1, %5 ; @21
+  %12 = lsl.w %rev.2, 0x3_w ; @27
+  %13 = lsl.w %rev.2, 0x1_w ; @28
+  %14 = add.w %12, %13 ; @29
+  %15 = add.w %14, %6 ; @30
+  jmp @3(%15, %4)
 @7:
-  %17 = eq.w %n, %rev.2 ; @32
-  %18 = flag.b %17 ; @33
-  ret %18
+  %18 = eq.w %n, %rev.2 ; @33
+  %19 = flag.b %18 ; @34
+  ret %19
 }
diff --git a/src/test/data/opt/palindrome.vir.opt.sysv.amd64.regalloc b/src/test/data/opt/palindrome.vir.opt.sysv.amd64.regalloc
index b703877a..770918d8 100644
--- a/src/test/data/opt/palindrome.vir.opt.sysv.amd64.regalloc
+++ b/src/test/data/opt/palindrome.vir.opt.sysv.amd64.regalloc
@@ -2,29 +2,30 @@ module palindrome
 
 export function $palindrome { ; returns: rax
 @2:
-  mov ecx, edi ; @50
-  xor eax, eax ; @51
-  mov edx, ecx ; @52
+  mov ecx, edi ; @52
+  xor eax, eax ; @53
+  mov edx, ecx ; @54
 @3:
-  test edx, edx ; @45
-  jne @6 ; @46
+  test edx, edx ; @47
+  jne @6 ; @48
 @7:
-  xor edx, edx ; @32
-  cmp ecx, eax ; @43
-  sete dl ; @44
-  mov al, dl ; @41
-  ret ; @42
+  xor edx, edx ; @33
+  cmp ecx, eax ; @45
+  sete dl ; @46
+  mov al, dl ; @43
+  ret ; @44
 @6:
-  imul rsi, rdx, 0x1999999a ; @16
-  shr rsi, 0x20_b ; @40
-  mov edi, esi ; @17
-  shr edi, 0x1f_b ; @39
-  add esi, edi ; @18
-  imul edi, esi, 0xa ; @19
-  sub edx, edi ; @38
-  lea edi, qword ptr [rax + rax*1] ; @27
-  lea eax, qword ptr [rdi + rax*8] ; @28
-  add eax, edx ; @29
-  mov edx, esi ; @35
-  jmp @3 ; @36
+  imul rdi, rdx, 0x66666667 ; @16
+  shr rdi, 0x20_b ; @42
+  mov esi, edi ; @17
+  sar esi, 0x2_b ; @41
+  shr edi, 0x1f_b ; @40
+  add esi, edi ; @19
+  imul edi, esi, 0xa ; @20
+  sub edx, edi ; @39
+  lea edi, qword ptr [rax + rax*1] ; @28
+  lea eax, qword ptr [rdi + rax*8] ; @29
+  add eax, edx ; @30
+  mov edx, esi ; @36
+  jmp @3 ; @37
 }
diff --git a/src/test/data/opt/sdivby11.vir.opt b/src/test/data/opt/sdivby11.vir.opt
index 1f780ab0..04364413 100644
--- a/src/test/data/opt/sdivby11.vir.opt
+++ b/src/test/data/opt/sdivby11.vir.opt
@@ -2,8 +2,9 @@ module foo
 
 export function w $foo(w %x) {
 @2:
-  %0 = mulh.w %x, 0x1745d175_w ; @4
-  %1 = lsr.w %0, 0x1f_w ; @5
-  %2 = add.w %0, %1 ; @6
-  ret %2
+  %0 = mulh.w %x, 0x2e8ba2e9_w ; @4
+  %1 = asr.w %0, 0x1_w ; @5
+  %2 = lsr.w %0, 0x1f_w ; @6
+  %3 = add.w %1, %2 ; @7
+  ret %3
 }
diff --git a/src/test/data/opt/sdivbyn5.vir.opt b/src/test/data/opt/sdivbyn5.vir.opt
index 053eac1b..dabcb3a5 100644
--- a/src/test/data/opt/sdivbyn5.vir.opt
+++ b/src/test/data/opt/sdivbyn5.vir.opt
@@ -2,8 +2,9 @@ module foo
 
 export function w $foo(w %x) {
 @2:
-  %0 = mulh.w %x, 0xcccccccc_w ; @4
-  %1 = lsr.w %0, 0x1f_w ; @5
-  %2 = add.w %0, %1 ; @6
-  ret %2
+  %0 = mulh.w %x, 0x99999999_w ; @4
+  %1 = asr.w %0, 0x1_w ; @5
+  %2 = lsr.w %0, 0x1f_w ; @6
+  %3 = add.w %1, %2 ; @7
+  ret %3
 }
diff --git a/src/test/data/opt/sdivbyn5.vir.opt.sysv.amd64.regalloc b/src/test/data/opt/sdivbyn5.vir.opt.sysv.amd64.regalloc
index 9396cab1..302db54c 100644
--- a/src/test/data/opt/sdivbyn5.vir.opt.sysv.amd64.regalloc
+++ b/src/test/data/opt/sdivbyn5.vir.opt.sysv.amd64.regalloc
@@ -2,11 +2,12 @@ module foo
 
 export function $foo { ; returns: rax
 @2:
-  mov eax, 0xcccccccc_w ; @10
-  imul rax, rdi ; @11
-  shr rax, 0x20_b ; @12
+  mov eax, 0x99999999_w ; @12
+  imul rax, rdi ; @13
+  shr rax, 0x20_b ; @14
   mov ecx, eax ; @5
-  shr ecx, 0x1f_b ; @9
-  add eax, ecx ; @6
-  ret ; @8
+  sar ecx, 0x1_b ; @11
+  shr eax, 0x1f_b ; @10
+  add eax, ecx ; @7
+  ret ; @9
 }
diff --git a/src/test/data/opt/sink1.vir.opt b/src/test/data/opt/sink1.vir.opt
index 8d310f66..b1ebe026 100644
--- a/src/test/data/opt/sink1.vir.opt
+++ b/src/test/data/opt/sink1.vir.opt
@@ -2,13 +2,10 @@ module sink1
 
 export function w $foo(w %x) {
 @2:
-  %2 = eq.w %x, 0x0_w ; @11
-  br %2, @3, @9(0x0_w)
-@3:
   %3 = add.w %x, 0x1_w ; @12
-  %4 = eq.w %3, 0x1_w ; @13
-  %5 = flag.w %4 ; @14
-  jmp @9(%5)
-@9(%0):
-  ret %0
+  %4 = eq.w %x, 0x0_w ; @13
+  %5 = eq.w %3, 0x1_w ; @14
+  %6 = flag.w %5 ; @15
+  %7 = sel.w %4, %6, 0x0_w ; @16
+  ret %7
 }
diff --git a/src/test/data/opt/sinking.vir.opt b/src/test/data/opt/sinking.vir.opt
index efd831a0..0adddeef 100644
--- a/src/test/data/opt/sinking.vir.opt
+++ b/src/test/data/opt/sinking.vir.opt
@@ -2,13 +2,10 @@ module foo
 
 export function w $foo(w %x, w %y) {
 @2:
-  %0 = add.w %x, 0x1_w ; @11
-  %3 = slt.w %x, 0x0_w ; @14
-  br %3, @3, @8(%y)
-@3:
-  %4 = lsl.w %0, 0x1_w ; @15
-  %5 = add.w %4, %y ; @16
-  jmp @8(%5)
-@8(%b.1):
-  ret %b.1
+  %1 = add.w %x, 0x1_w ; @12
+  %2 = lsl.w %1, 0x1_w ; @13
+  %5 = slt.w %x, 0x0_w ; @16
+  %6 = add.w %2, %y ; @17
+  %8 = sel.w %5, %6, %y ; @19
+  ret %8
 }
diff --git a/src/test/data/opt/sremby7.vir.opt b/src/test/data/opt/sremby7.vir.opt
index f0a40cbd..3a60c5e0 100644
--- a/src/test/data/opt/sremby7.vir.opt
+++ b/src/test/data/opt/sremby7.vir.opt
@@ -2,11 +2,12 @@ module foo
 
 export function w $foo(w %x) {
 @2:
-  %0 = mulh.w %x, 0x24924925_w ; @4
-  %1 = lsr.w %0, 0x1f_w ; @5
-  %2 = add.w %0, %1 ; @6
-  %3 = lsl.w %2, 0x3_w ; @7
-  %4 = sub.w %x, %3 ; @8
-  %5 = add.w %4, %2 ; @9
-  ret %5
+  %0 = mulh.w %x, 0x92492493_w ; @4
+  %1 = add.w %0, %x ; @5
+  %2 = asr.w %1, 0x2_w ; @6
+  %3 = lsr.w %1, 0x1f_w ; @7
+  %4 = add.w %2, %3 ; @8
+  %5 = mul.w %4, 0x7_w ; @9
+  %6 = sub.w %x, %5 ; @10
+  ret %6
 }
diff --git a/src/test/data/opt/sremby7.vir.opt.sysv.amd64.regalloc b/src/test/data/opt/sremby7.vir.opt.sysv.amd64.regalloc
index abac14f4..8e2409f1 100644
--- a/src/test/data/opt/sremby7.vir.opt.sysv.amd64.regalloc
+++ b/src/test/data/opt/sremby7.vir.opt.sysv.amd64.regalloc
@@ -2,14 +2,16 @@ module foo
 
 export function $foo { ; returns: rax
 @2:
-  imul rax, rdi, 0x24924925 ; @16
-  shr rax, 0x20_b ; @17
-  mov ecx, eax ; @5
-  shr ecx, 0x1f_b ; @15
-  add eax, ecx ; @6
-  mov ecx, eax ; @7
-  shl ecx, 0x3_b ; @14
-  sub edi, ecx ; @13
-  add eax, edi ; @9
-  ret ; @12
+  mov eax, edi ; @4
+  mov ecx, 0x92492493_w ; @18
+  imul rcx, edi ; @19
+  shr rcx, 0x20_b ; @20
+  lea edx, qword ptr [rcx + rax*1] ; @5
+  mov ecx, edx ; @6
+  sar ecx, 0x2_b ; @17
+  shr edx, 0x1f_b ; @16
+  add ecx, edx ; @8
+  imul ecx, ecx, 0x7 ; @9
+  sub eax, ecx ; @15
+  ret ; @14
 }
diff --git a/src/test/data/opt/switchsimpl.vir.opt b/src/test/data/opt/switchsimpl.vir.opt
index 79defcc1..3ecf1365 100644
--- a/src/test/data/opt/switchsimpl.vir.opt
+++ b/src/test/data/opt/switchsimpl.vir.opt
@@ -3,10 +3,7 @@ module foo
 export function w $foo(w %x) {
 @2:
   %2 = eq.w %x, 0x1_w ; @9
-  br %2, @7(0x2_w), @3
-@3:
   %3 = sub.w %x, 0x1_w ; @10
-  jmp @7(%3)
-@7(%0):
-  ret %0
+  %4 = sel.w %2, 0x2_w, %3 ; @11
+  ret %4
 }
diff --git a/src/test/test_opt.ml b/src/test/test_opt.ml
index 84da395f..5bc123f0 100644
--- a/src/test/test_opt.ml
+++ b/src/test/test_opt.ml
@@ -333,6 +333,7 @@ let opt_suite = "Test optimizations" >::: [
     "Bad load 1" >:: test "badload1";
     "Bad load 2" >:: test "badload2";
     "Binary search" >:: test "bsearch";
+    "If-conversion 1" >:: test "ifc1";
   ]
 
 let abi_suite = "Test ABI lowering" >::: [