diff --git a/pytools/obj_array.py b/pytools/obj_array.py
index c8b48e5f..29069647 100644
--- a/pytools/obj_array.py
+++ b/pytools/obj_array.py
@@ -162,19 +162,29 @@ def __getitem__(self: ObjectArrayND[T], x: int, /) -> ObjectArrayND[T] | T: ...
 
         @overload
         def __getitem__(
-                self: ObjectArrayND[T],
-                x: tuple[int | slice, ...],
-            /) -> ObjectArrayND[T] | T: ...
+            self: ObjectArray1D[T],
+            x: slice, /) -> ObjectArray1D[T]: ...
 
         @overload
         def __getitem__(
-            self: ObjectArray1D[T],
-            x: slice) -> ObjectArray1D[T]: ...
+            self: ObjectArray2D[T],
+            x: slice, /) -> ObjectArray2D[T]: ...
+
+        @overload
+        def __getitem__(
+            self: ObjectArray2D[T],
+            x: tuple[slice, int], /) -> ObjectArray1D[T]: ...
 
         @overload
         def __getitem__(
             self: ObjectArray2D[T],
-            x: slice) -> ObjectArray2D[T]: ...
+            x: tuple[int, slice], /) -> ObjectArray1D[T]: ...
+
+        @overload
+        def __getitem__(
+                self: ObjectArrayND[T],
+                x: tuple[int | slice, ...],
+            /) -> ObjectArrayND[T] | T: ...
 
         @overload
         def __iter__(self: ObjectArray1D[T]) -> Iterator[T]: ...
@@ -406,6 +416,38 @@ def trace(
     return cast("T", np.trace(cast("NDArray[Any]", cast("object", array))))
 
 
+@overload
+def sum(
+            array: ObjectArrayND[T],
+            axis: None,
+        ) -> T: ...
+
+
+@overload
+def sum(
+            array: ObjectArray1D[T],
+            axis: int,
+        ) -> T: ...
+
+
+@overload
+def sum(
+            array: ObjectArray2D[T],
+            axis: int,
+        ) -> ObjectArray1D[T]: ...
+
+
+def sum(
+            array: ObjectArrayND[T],
+            axis: int | None,
+        ) -> ObjectArrayND[T] | T:
+    import numpy as np
+    return cast("ObjectArrayND[T] | T", np.sum(
+            cast("NDArray[Any]", cast("object", array)),
+            axis=axis,
+        ))
+
+
 def to_hashable(ary: ObjectArray[ShapeT, T] | Hashable, /) -> Hashable:
     if isinstance(ary, ObjectArray):
         ary = cast("ObjectArray[ShapeT, T]", ary)