diff --git a/utils/retriangulate.cpp b/utils/retriangulate.cpp
index 5d8d194fe..f945a982c 100644
--- a/utils/retriangulate.cpp
+++ b/utils/retriangulate.cpp
@@ -51,16 +51,19 @@ enum {
     FLAVOUR_KNOT = 100
 } flavour = FLAVOUR_NONE;
 bool internalSig = false;
+bool exhaustive = false;
 
 template <int dim>
 void process(const regina::Triangulation<dim>& tri) {
     unsigned long nSolns = 0;
+	unsigned long total = 0;
     bool nonMinimal = false;
     std::string simpler;
 
     tri.retriangulate(argHeight, argThreads, nullptr /* tracker */,
-        [&nSolns, &nonMinimal, &simpler, &tri](
+					  [&total, &nSolns, &nonMinimal, &simpler, &tri](
                 const std::string& sig, const regina::Triangulation<dim>& t) {
+			++total;
             if (t.size() > tri.size())
                 return false;
 
@@ -71,7 +74,8 @@ void process(const regina::Triangulation<dim>& tri) {
                 if (t.size() < tri.size()) {
                     nonMinimal = true;
                     simpler = sig;
-                    return true;
+					if (!exhaustive)
+						return true;
                 }
 
                 ++nSolns;
@@ -86,7 +90,8 @@ void process(const regina::Triangulation<dim>& tri) {
                 if (t.size() < tri.size()) {
                     nonMinimal = true;
                     simpler = std::move(classic);
-                    return true;
+					if (!exhaustive)
+						return true;
                 }
 
                 ++nSolns;
@@ -97,8 +102,10 @@ void process(const regina::Triangulation<dim>& tri) {
     if (nonMinimal) {
         std::cerr << "Triangulation is non-minimal!" << std::endl;
         std::cerr << "Smaller triangulation: " << simpler << std::endl;
-    } else
-        std::cerr << "Found " << nSolns << " triangulation(s)." << std::endl;
+    }
+	if (!nonMinimal || exhaustive)
+		std::cerr << "Found " << nSolns << " triangulation(s)." << std::endl;
+	std::cerr << "Considered " << total << " triangulations." << std::endl;
 }
 
 void process(const regina::Link& knot) {
@@ -141,6 +148,7 @@ R"help(Usage: retriangulate <isosig>
   -4, --dim4                  Input is a 4-manifold signature
   -k, --knot                  Input is a knot signature
   -a, --anysig                Output does not need to use classic signature(s)
+  -e, --exhaustive            Do not stop when encountering smaller signature
   -v, --version               Show which version of Regina is being used.
       --help                  Show this help message
 )help";
@@ -148,7 +156,7 @@ R"help(Usage: retriangulate <isosig>
 
 int main(int argc, char* argv[]) {
     // Parse the command-line arguments.
-    const char* shortOpt = ":h:t:34kav";
+    const char* shortOpt = ":h:t:34kave";
     struct option longOpt[] = {
         { "height", required_argument, nullptr, 'h' },
         { "threads", required_argument, nullptr, 't' },
@@ -156,6 +164,7 @@ int main(int argc, char* argv[]) {
         { "dim4", no_argument, nullptr, '4' },
         { "knot", no_argument, nullptr, 'k' },
         { "anysig", no_argument, nullptr, 'a' },
+		{ "exhaustive", no_argument, nullptr, 'e' },
         { "version", no_argument, nullptr, 'v' },
         { "help", no_argument, nullptr, '_' },
         { nullptr, 0, nullptr, 0 }
@@ -213,6 +222,9 @@ int main(int argc, char* argv[]) {
             case 'a':
                 internalSig = true;
                 break;
+		    case 'e' :
+				exhaustive = true;
+				break;
             case 'v':
                 // If other arguments were passed, just silently ignore them
                 // for now.  Ideally we would give an error in this scenario.