diff --git a/scripts/test/fuzzing.py b/scripts/test/fuzzing.py
index 0f4a1befa74..0bbfbcd9717 100644
--- a/scripts/test/fuzzing.py
+++ b/scripts/test/fuzzing.py
@@ -105,6 +105,7 @@
     'exact-references.wast',
     'optimize-instructions-exact.wast',
     'local-subtyping-exact.wast',
+    'remove-unused-types-exact.wast',
 ]
 
 
diff --git a/src/ir/type-updating.cpp b/src/ir/type-updating.cpp
index b90d8eb8790..cba761465b3 100644
--- a/src/ir/type-updating.cpp
+++ b/src/ir/type-updating.cpp
@@ -205,7 +205,9 @@ void GlobalTypeRewriter::mapTypes(const TypeMap& oldToNewTypes) {
 
     Type getNew(Type type) {
       if (type.isRef()) {
-        return Type(getNew(type.getHeapType()), type.getNullability());
+        return Type(getNew(type.getHeapType()),
+                    type.getNullability(),
+                    type.getExactness());
       }
       if (type.isTuple()) {
         auto tuple = type.getTuple();
diff --git a/src/wasm-type.h b/src/wasm-type.h
index f09e1e440fe..a33a2bed907 100644
--- a/src/wasm-type.h
+++ b/src/wasm-type.h
@@ -709,7 +709,8 @@ struct TypeBuilder {
         return t;
       }
       assert(t.isRef());
-      return getTempRefType(map(t.getHeapType()), t.getNullability());
+      return getTempRefType(
+        map(t.getHeapType()), t.getNullability(), t.getExactness());
     };
     auto copyType = [&](Type t) -> Type {
       if (t.isTuple()) {
diff --git a/test/lit/passes/remove-unused-types-exact.wast b/test/lit/passes/remove-unused-types-exact.wast
new file mode 100644
index 00000000000..6cb9c1ddd74
--- /dev/null
+++ b/test/lit/passes/remove-unused-types-exact.wast
@@ -0,0 +1,16 @@
+;; NOTE: Assertions have been generated by update_lit_checks.py and should not be edited.
+
+;; RUN: wasm-opt %s -all --closed-world --remove-unused-types -S -o - | filecheck %s
+
+;; Test that a simple type rewrite handles exact references in heap type
+;; definitions correctly. In particular, the function should continue returning
+;; an exact nullref and the call expression should have the same type.
+
+(module
+  ;; CHECK:      (func $return-exact (type $0) (result (exact nullref))
+  ;; CHECK-NEXT:  (call $return-exact)
+  ;; CHECK-NEXT: )
+  (func $return-exact (result (exact nullref))
+    (call $return-exact)
+  )
+)