diff --git a/src/hb-open-type.hh b/src/hb-open-type.hh
index 8c4271b68..478bb60ac 100644
--- a/src/hb-open-type.hh
+++ b/src/hb-open-type.hh
@@ -53,7 +53,7 @@ namespace OT {
  */
 
 /* Integer types in big-endian order and no alignment requirement */
-template <typename Type, unsigned int Size>
+template <typename Type, unsigned int Size = sizeof (Type)>
 struct IntType
 {
   typedef Type type;
@@ -107,12 +107,12 @@ struct IntType
   DEFINE_SIZE_STATIC (Size);
 };
 
-typedef IntType<uint8_t,  1> HBUINT8;	/* 8-bit unsigned integer. */
-typedef IntType<int8_t,   1> HBINT8;	/* 8-bit signed integer. */
-typedef IntType<uint16_t, 2> HBUINT16;	/* 16-bit unsigned integer. */
-typedef IntType<int16_t,  2> HBINT16;	/* 16-bit signed integer. */
-typedef IntType<uint32_t, 4> HBUINT32;	/* 32-bit unsigned integer. */
-typedef IntType<int32_t,  4> HBINT32;	/* 32-bit signed integer. */
+typedef IntType<uint8_t>  HBUINT8;	/* 8-bit unsigned integer. */
+typedef IntType<int8_t>   HBINT8;	/* 8-bit signed integer. */
+typedef IntType<uint16_t> HBUINT16;	/* 16-bit unsigned integer. */
+typedef IntType<int16_t>  HBINT16;	/* 16-bit signed integer. */
+typedef IntType<uint32_t> HBUINT32;	/* 32-bit unsigned integer. */
+typedef IntType<int32_t>  HBINT32;	/* 32-bit signed integer. */
 /* Note: we cannot defined a signed HBINT24 because there's no corresponding C type.
  * Works for unsigned, but not signed, since we rely on compiler for sign-extension. */
 typedef IntType<uint32_t, 3> HBUINT24;	/* 24-bit unsigned integer. */
diff --git a/src/hb-serialize.hh b/src/hb-serialize.hh
index 7238fb0d8..fe29bdf96 100644
--- a/src/hb-serialize.hh
+++ b/src/hb-serialize.hh
@@ -524,7 +524,7 @@ struct hb_serialize_context_t
   template <typename T>
   void assign_offset (const object_t* parent, const object_t::link_t &link, unsigned offset)
   {
-    auto &off = * ((BEInt<T, sizeof (T)> *) (parent->head + link.position));
+    auto &off = * ((BEInt<T> *) (parent->head + link.position));
     assert (0 == off);
     check_assign (off, offset);
   }
diff --git a/src/hb.hh b/src/hb.hh
index f569fbfc7..fe6ffc873 100644
--- a/src/hb.hh
+++ b/src/hb.hh
@@ -464,10 +464,10 @@ static inline constexpr uint32_t hb_uint32_swap (uint32_t v)
 { return (hb_uint16_swap (v) << 16) | hb_uint16_swap (v >> 16); }
 
 /*
- * Big-endian integers.  Here because fundamental.
+ * Big-endian integers.
  */
 
-template <typename Type, int Bytes> struct BEInt;
+template <typename Type, int Bytes = sizeof (Type)> struct BEInt;
 
 template <typename Type>
 struct BEInt<Type, 1>