diff --git a/asyncpg/protocol/codecs/base.pyx b/asyncpg/protocol/codecs/base.pyx
index 2da74249..70aa650e 100644
--- a/asyncpg/protocol/codecs/base.pyx
+++ b/asyncpg/protocol/codecs/base.pyx
@@ -474,10 +474,6 @@ cdef class DataCodecConfig:
                          encoder, decoder, binary):
         format = PG_FORMAT_BINARY if binary else PG_FORMAT_TEXT
 
-        if self.get_codec(typeoid, format) is not None:
-            raise ValueError('cannot override codec for type {}'.format(
-                typeoid))
-
         self._local_type_codecs[typeoid, format] = \
             Codec.new_python_codec(typeoid, typename, typeschema, typekind,
                                    encoder, decoder, format)
@@ -519,17 +515,17 @@ cdef class DataCodecConfig:
     cdef inline Codec get_codec(self, uint32_t oid, CodecFormat format):
         cdef Codec codec
 
-        codec = get_core_codec(oid, format)
-        if codec is not None:
-            return codec
-
         try:
-            return self._type_codecs_cache[oid, format]
+            return self._local_type_codecs[oid, format]
         except KeyError:
-            try:
-                return self._local_type_codecs[oid, format]
-            except KeyError:
-                return None
+            codec = get_core_codec(oid, format)
+            if codec is not None:
+                return codec
+            else:
+                try:
+                    return self._type_codecs_cache[oid, format]
+                except KeyError:
+                    return None
 
 
 cdef inline Codec get_core_codec(uint32_t oid, CodecFormat format):
diff --git a/tests/test_codecs.py b/tests/test_codecs.py
index ec8356e5..a810bd00 100644
--- a/tests/test_codecs.py
+++ b/tests/test_codecs.py
@@ -900,6 +900,30 @@ def hstore_encoder(obj):
                 DROP EXTENSION hstore
             ''')
 
+    async def test_custom_codec_override(self):
+        """Test overriding core codecs."""
+        import json
+
+        conn = await self.cluster.connect(database='postgres', loop=self.loop)
+        try:
+            def _encoder(value):
+                return json.dumps(value).encode('utf-8')
+
+            def _decoder(value):
+                return json.loads(value.decode('utf-8'))
+
+            await conn.set_type_codec(
+                'json', encoder=_encoder, decoder=_decoder,
+                schema='pg_catalog', binary=True
+            )
+
+            data = {'foo': 'bar', 'spam': 1}
+            res = await conn.fetchval('SELECT $1::json', data)
+            self.assertEqual(data, res)
+
+        finally:
+            await conn.close()
+
     async def test_composites_in_arrays(self):
         await self.con.execute('''
             CREATE TYPE t AS (a text, b int);
diff --git a/tests/test_connect.py b/tests/test_connect.py
index 09c987e7..5d54fac5 100644
--- a/tests/test_connect.py
+++ b/tests/test_connect.py
@@ -96,9 +96,21 @@ def tearDown(self):
     async def test_auth_bad_user(self):
         with self.assertRaises(
                 asyncpg.InvalidAuthorizationSpecificationError):
-            await self.cluster.connect(user='__nonexistent__',
-                                       database='postgres',
-                                       loop=self.loop)
+            for tried in range(3):
+                try:
+                    await self.cluster.connect(user='__nonexistent__',
+                                               database='postgres',
+                                               loop=self.loop)
+                except asyncpg.ConnectionDoesNotExistError:
+                    if _system == 'Windows':
+                        # On Windows the server sometimes just closes
+                        # the connection sooner than we receive the
+                        # actual error.
+                        continue
+                    else:
+                        raise
+                else:
+                    break
 
     async def test_auth_trust(self):
         conn = await self.cluster.connect(