diff --git a/src/hb-map.hh b/src/hb-map.hh
index a0ab17a23..c62b9d7bb 100644
--- a/src/hb-map.hh
+++ b/src/hb-map.hh
@@ -35,9 +35,7 @@
  */
 
 template <typename K, typename V,
-	  typename k_invalid_t = K,
 	  typename v_invalid_t = V,
-	  k_invalid_t kINVALID = std::is_pointer<K>::value ? 0 : std::is_signed<K>::value ? hb_int_min (K) : (K) -1,
 	  v_invalid_t vINVALID = std::is_pointer<V>::value ? 0 : std::is_signed<V>::value ? hb_int_min (V) : (V) -1>
 struct hb_hashmap_t
 {
@@ -401,15 +399,11 @@ struct hb_hashmap_t
 struct hb_map_t : hb_hashmap_t<hb_codepoint_t,
 			       hb_codepoint_t,
 			       hb_codepoint_t,
-			       hb_codepoint_t,
-			       HB_MAP_VALUE_INVALID,
 			       HB_MAP_VALUE_INVALID>
 {
   using hashmap = hb_hashmap_t<hb_codepoint_t,
 			       hb_codepoint_t,
 			       hb_codepoint_t,
-			       hb_codepoint_t,
-			       HB_MAP_VALUE_INVALID,
 			       HB_MAP_VALUE_INVALID>;
 
   ~hb_map_t () = default;
diff --git a/src/hb-ot-post-table-v2subset.hh b/src/hb-ot-post-table-v2subset.hh
index c817b28e6..8c0312fa4 100644
--- a/src/hb-ot-post-table-v2subset.hh
+++ b/src/hb-ot-post-table-v2subset.hh
@@ -78,7 +78,7 @@ HB_INTERNAL bool postV2Tail::subset (hb_subset_context_t *c) const
 
   post::accelerator_t _post (c->plan->source);
 
-  hb_hashmap_t<hb_bytes_t, unsigned, std::nullptr_t, unsigned, nullptr, (unsigned)-1> glyph_name_to_new_index;
+  hb_hashmap_t<hb_bytes_t, unsigned> glyph_name_to_new_index;
   for (hb_codepoint_t new_gid = 0; new_gid < num_glyphs; new_gid++)
   {
     hb_codepoint_t old_gid = reverse_glyph_map.get (new_gid);
diff --git a/src/hb-serialize.hh b/src/hb-serialize.hh
index 5663b290c..3f4535ce4 100644
--- a/src/hb-serialize.hh
+++ b/src/hb-serialize.hh
@@ -720,8 +720,7 @@ struct hb_serialize_context_t
 
   /* Map view of packed objects. */
   hb_hashmap_t<const object_t *, objidx_t,
-	       const object_t *, objidx_t,
-	       nullptr, 0> packed_map;
+	       objidx_t, 0> packed_map;
 };
 
 #endif /* HB_SERIALIZE_HH */
diff --git a/src/test-map.cc b/src/test-map.cc
index a5e85074c..e62f65091 100644
--- a/src/test-map.cc
+++ b/src/test-map.cc
@@ -127,19 +127,19 @@ main (int argc, char **argv)
 
   /* Test class key / value types. */
   {
-    hb_hashmap_t<hb_bytes_t, int, std::nullptr_t, int, nullptr, 0> m1;
-    hb_hashmap_t<int, hb_bytes_t, int, std::nullptr_t, 0, nullptr> m2;
-    hb_hashmap_t<hb_bytes_t, hb_bytes_t, std::nullptr_t, std::nullptr_t, nullptr, nullptr> m3;
+    hb_hashmap_t<hb_bytes_t, int, int, 0> m1;
+    hb_hashmap_t<int, hb_bytes_t, std::nullptr_t, nullptr> m2;
+    hb_hashmap_t<hb_bytes_t, hb_bytes_t, std::nullptr_t, nullptr> m3;
     assert (m1.get_population () == 0);
     assert (m2.get_population () == 0);
     assert (m3.get_population () == 0);
   }
 
   {
-    hb_hashmap_t<int, int, int, int, 0, 0> m0;
-    hb_hashmap_t<std::string, int, const std::string*, int, &invalid, 0> m1;
-    hb_hashmap_t<int, std::string, int, const std::string*, 0, &invalid> m2;
-    hb_hashmap_t<std::string, std::string, const std::string*, const std::string*, &invalid, &invalid> m3;
+    hb_hashmap_t<int, int, int, 0> m0;
+    hb_hashmap_t<std::string, int, int, 0> m1;
+    hb_hashmap_t<int, std::string, const std::string*, &invalid> m2;
+    hb_hashmap_t<std::string, std::string, const std::string*, &invalid> m3;
 
     std::string s;
     for (unsigned i = 1; i < 1000; i++)
@@ -156,8 +156,8 @@ main (int argc, char **argv)
   {
     using pair = hb_pair_t<hb_codepoint_t, hb_codepoint_t>;
 
-    hb_hashmap_t<hb_map_t, hb_map_t, const hb_map_t *, const hb_map_t *, &invalid_map, &invalid_map> m1;
-    hb_hashmap_t<hb_map_t, hb_map_t, std::nullptr_t, std::nullptr_t, nullptr, nullptr> m2;
+    hb_hashmap_t<hb_map_t, hb_map_t, const hb_map_t *, &invalid_map> m1;
+    hb_hashmap_t<hb_map_t, hb_map_t, std::nullptr_t, nullptr> m2;
 
     m1.set (hb_map_t (), hb_map_t {});
     m2.set (hb_map_t (), hb_map_t {});
@@ -177,8 +177,8 @@ main (int argc, char **argv)
 
   /* Test hashing sets. */
   {
-    hb_hashmap_t<hb_set_t, hb_set_t, const hb_set_t *, const hb_set_t *, &invalid_set, &invalid_set> m1;
-    hb_hashmap_t<hb_set_t, hb_set_t, std::nullptr_t, std::nullptr_t, nullptr, nullptr> m2;
+    hb_hashmap_t<hb_set_t, hb_set_t, const hb_set_t *, &invalid_set> m1;
+    hb_hashmap_t<hb_set_t, hb_set_t, std::nullptr_t, nullptr> m2;
 
     m1.set (hb_set_t (), hb_set_t ());
     m2.set (hb_set_t (), hb_set_t ());
@@ -200,8 +200,8 @@ main (int argc, char **argv)
   {
     using vector_t = hb_vector_t<unsigned>;
 
-    hb_hashmap_t<vector_t, vector_t, const vector_t *, const vector_t *, &invalid_vector, &invalid_vector> m1;
-    hb_hashmap_t<vector_t, vector_t, std::nullptr_t, std::nullptr_t, nullptr, nullptr> m2;
+    hb_hashmap_t<vector_t, vector_t, const vector_t *, &invalid_vector> m1;
+    hb_hashmap_t<vector_t, vector_t, std::nullptr_t, nullptr> m2;
 
     m1.set (vector_t (), vector_t ());
     m2.set (vector_t (), vector_t ());