diff --git a/src/hb-map-private.hh b/src/hb-map-private.hh
index 46634465d..cad6f0e2d 100644
--- a/src/hb-map-private.hh
+++ b/src/hb-map-private.hh
@@ -98,7 +98,6 @@ struct hb_map_t
   };
 
   hb_object_header_t header;
-  ASSERT_POD ();
   bool successful; /* Allocations successful */
   unsigned int population; /* Not including tombstones. */
   unsigned int occupancy; /* Including tombstones. */
@@ -252,7 +251,7 @@ struct hb_map_t
   }
 
   private:
-  HB_DISALLOW_ASSIGN (hb_map_t);
+  HB_DISALLOW_COPY_AND_ASSIGN (hb_map_t);
 };
 
 
diff --git a/src/hb-ot-shape-private.hh b/src/hb-ot-shape-private.hh
index a540e6afa..c217af0c0 100644
--- a/src/hb-ot-shape-private.hh
+++ b/src/hb-ot-shape-private.hh
@@ -99,7 +99,7 @@ struct hb_ot_shape_planner_t
   }
 
   private:
-  HB_DISALLOW_ASSIGN (hb_ot_shape_planner_t);
+  HB_DISALLOW_COPY_AND_ASSIGN (hb_ot_shape_planner_t);
 };
 
 
diff --git a/src/hb-private.hh b/src/hb-private.hh
index 53dfd8086..05f0adbe5 100644
--- a/src/hb-private.hh
+++ b/src/hb-private.hh
@@ -537,7 +537,11 @@ _hb_ceil_to_4 (unsigned int v)
  */
 
 #define HB_DISALLOW_ASSIGN(TypeName) \
-  void operator=(const TypeName&)
+  void operator=(const TypeName&) = delete
+
+#define HB_DISALLOW_COPY_AND_ASSIGN(TypeName) \
+  TypeName(const TypeName&) = delete; \
+  void operator=(const TypeName&) = delete
 
 /*
  * Static pools
diff --git a/src/hb-set-private.hh b/src/hb-set-private.hh
index 0129af87e..323c6f4ba 100644
--- a/src/hb-set-private.hh
+++ b/src/hb-set-private.hh
@@ -180,7 +180,6 @@ struct hb_set_t
   static_assert (page_t::PAGE_BITS == sizeof (page_t) * 8, "");
 
   hb_object_header_t header;
-  ASSERT_POD ();
   bool successful; /* Allocations successful */
   mutable unsigned int population;
   hb_vector_t<page_map_t, 8> page_map;
@@ -679,7 +678,7 @@ struct hb_set_t
   inline hb_codepoint_t major_start (unsigned int major) const { return major * page_t::PAGE_BITS; }
 
   private:
-  HB_DISALLOW_ASSIGN (hb_set_t);
+  HB_DISALLOW_COPY_AND_ASSIGN (hb_set_t);
 };