diff --git a/regression-tests/pure2-bugfix-for-deducible-parameters.cpp2 b/regression-tests/pure2-bugfix-for-deducible-parameters.cpp2
index 0a9565f36..cd371175b 100644
--- a/regression-tests/pure2-bugfix-for-deducible-parameters.cpp2
+++ b/regression-tests/pure2-bugfix-for-deducible-parameters.cpp2
@@ -18,8 +18,15 @@ main: () = {
   _ = :<T> (x: std::vector<std::vector<T>>) = {}(:std::vector<std::vector<i32>> = ());
   // Uncomment once `typename` is supported for template arguments.
   // _ = :<T, U> (x: std::pair<T, typename U::value_type>, y: U) = {}(:std::pair = (0, 0), z);
+  _ = :<T, U> (x: std::array<T, U::value>, y: U) = {}(:std::array<i32, 0> = (), z);
   init(out z, z);
   id(z, z);
+
+  // Test that these are emitted unwrapped in case they are deducible.
+  (copy f := :<T> (x: std::vector<std::type_identity_t<T>>) = {})
+    static_assert(!std::is_invocable_v<decltype(f), std::vector<i32>>);
+  (copy f := :<T> (x: std::vector<std::vector<T>>) = {})
+    static_assert(std::is_invocable_v<decltype(f), std::vector<std::vector<i32>>>);
 }
 
 v: <T> type = {
diff --git a/regression-tests/test-results/pure2-bugfix-for-deducible-parameters.cpp b/regression-tests/test-results/pure2-bugfix-for-deducible-parameters.cpp
index d4d843bd7..5a8530703 100644
--- a/regression-tests/test-results/pure2-bugfix-for-deducible-parameters.cpp
+++ b/regression-tests/test-results/pure2-bugfix-for-deducible-parameters.cpp
@@ -7,7 +7,7 @@
 #include "cpp2util.h"
 
 
-#line 25 "pure2-bugfix-for-deducible-parameters.cpp2"
+#line 32 "pure2-bugfix-for-deducible-parameters.cpp2"
 template<typename T> class v;
   
 
@@ -24,15 +24,15 @@ template<typename T> auto id(cpp2::in<std::integral_constant<cpp2::i32,T::value>
 auto main() -> int;
   
 
-#line 25 "pure2-bugfix-for-deducible-parameters.cpp2"
+#line 32 "pure2-bugfix-for-deducible-parameters.cpp2"
 template<typename T> class v {
   public: explicit v(T const& x);
-#line 26 "pure2-bugfix-for-deducible-parameters.cpp2"
+#line 33 "pure2-bugfix-for-deducible-parameters.cpp2"
   public: auto operator=(T const& x) -> v& ;
 
   public: v(v const&) = delete; /* No 'that' constructor, suppress copy */
   public: auto operator=(v const&) -> void = delete;
-#line 27 "pure2-bugfix-for-deducible-parameters.cpp2"
+#line 34 "pure2-bugfix-for-deducible-parameters.cpp2"
 };
 
 
@@ -58,15 +58,31 @@ auto main() -> int{
   (void) []<typename T>(std::vector<std::vector<T>> const& x) -> void{}(std::vector<std::vector<cpp2::i32>>{});
   // Uncomment once `typename` is supported for template arguments.
   // _ = :<T, U> (x: std::pair<T, typename U::value_type>, y: U) = {}(:std::pair = (0, 0), z);
+  (void) []<typename T, typename U>(std::array<T,U::value> const& x, U const& y) -> void{}(std::array<cpp2::i32,0>{}, z.value());
   init(cpp2::out(&z.value()), z.value());
   id(z.value(), std::move(z.value()));
+{
+auto f = []<typename T>(std::vector<std::type_identity_t<T>> const& x) -> void{};
+
+  // Test that these are emitted unwrapped in case they are deducible.
+
+#line 27 "pure2-bugfix-for-deducible-parameters.cpp2"
+    static_assert(!(std::is_invocable_v<decltype(f),std::vector<cpp2::i32>>));
+}
+{
+auto f = []<typename T>(std::vector<std::vector<T>> const& x) -> void{};
+
+#line 29 "pure2-bugfix-for-deducible-parameters.cpp2"
+    static_assert(std::is_invocable_v<decltype(f),std::vector<std::vector<cpp2::i32>>>);
+}
+#line 30 "pure2-bugfix-for-deducible-parameters.cpp2"
 }
 
-#line 26 "pure2-bugfix-for-deducible-parameters.cpp2"
+#line 33 "pure2-bugfix-for-deducible-parameters.cpp2"
   template <typename T> v<T>::v(T const& x){}
-#line 26 "pure2-bugfix-for-deducible-parameters.cpp2"
+#line 33 "pure2-bugfix-for-deducible-parameters.cpp2"
   template <typename T> auto v<T>::operator=(T const& x) -> v& {
                                   return *this;
-#line 26 "pure2-bugfix-for-deducible-parameters.cpp2"
+#line 33 "pure2-bugfix-for-deducible-parameters.cpp2"
   }