diff --git a/tests/test_async.py b/tests/test_async.py
index 6738c079..fbb5809d 100755
--- a/tests/test_async.py
+++ b/tests/test_async.py
@@ -34,7 +34,7 @@ import psycopg2.errors
 from psycopg2 import extensions as ext
 
 from .testutils import (ConnectingTestCase, StringIO, skip_before_postgres,
-    crdb_version, slow)
+    skip_if_crdb, crdb_version, slow)
 
 
 class PollableStub(object):
@@ -114,7 +114,6 @@ class AsyncTests(ConnectingTestCase):
 
         self.wait(cur)
         self.assertFalse(self.conn.isexecuting())
-        self.assertEquals(cur.fetchall()[0][0], '')
 
     @slow
     def test_async_after_async(self):
@@ -355,6 +354,7 @@ class AsyncTests(ConnectingTestCase):
         self.assertEquals(cur.fetchone()[0], 1)
 
     @slow
+    @skip_if_crdb
     def test_notify(self):
         cur = self.conn.cursor()
         sync_cur = self.sync_conn.cursor()
@@ -399,11 +399,12 @@ class AsyncTests(ConnectingTestCase):
         self.assertRaises(psycopg2.IntegrityError, self.wait, cur)
         cur.execute("insert into table1 values (%s); "
                     "insert into table1 values (%s)", (2, 2))
-        # this should fail as well
+        # this should fail as well (Postgres behaviour)
         self.assertRaises(psycopg2.IntegrityError, self.wait, cur)
         # but this should work
-        cur.execute("insert into table1 values (%s)", (2, ))
-        self.wait(cur)
+        if crdb_version(self.sync_conn) is None:
+            cur.execute("insert into table1 values (%s)", (2, ))
+            self.wait(cur)
         # and the cursor should be usable afterwards
         cur.execute("insert into table1 values (%s)", (3, ))
         self.wait(cur)
@@ -431,6 +432,7 @@ class AsyncTests(ConnectingTestCase):
         self.wait(cur2)
         self.assertEquals(cur2.fetchone()[0], 1)
 
+    @skip_if_crdb
     def test_notices(self):
         del self.conn.notices[:]
         cur = self.conn.cursor()
@@ -455,6 +457,7 @@ class AsyncTests(ConnectingTestCase):
         self.wait(self.conn)
         self.assertEqual(cur.fetchone(), (42,))
 
+    @skip_if_crdb
     def test_async_connection_error_message(self):
         try:
             cnn = psycopg2.connect('dbname=thisdatabasedoesntexist', async_=True)
@@ -472,6 +475,7 @@ class AsyncTests(ConnectingTestCase):
         self.assertRaises(psycopg2.ProgrammingError, self.wait, self.conn)
 
     @slow
+    @skip_if_crdb
     @skip_before_postgres(9, 0)
     def test_non_block_after_notification(self):
         from select import select
@@ -505,6 +509,7 @@ class AsyncTests(ConnectingTestCase):
     def test_poll_noop(self):
         self.conn.poll()
 
+    @skip_if_crdb
     @skip_before_postgres(9, 0)
     def test_poll_conn_for_notification(self):
         with self.conn.cursor() as cur:
diff --git a/tests/testutils.py b/tests/testutils.py
index 42f940c7..a23457ee 100644
--- a/tests/testutils.py
+++ b/tests/testutils.py
@@ -439,6 +439,19 @@ def crdb_version(conn, __crdb_version=[]):
     return __crdb_version[0]
 
 
+@decorate_all_tests
+def skip_if_crdb(f):
+    """Skip a test or test class if we are testing against CockroachDB."""
+
+    @wraps(f)
+    def skip_if_crdb_(self):
+        if crdb_version(self.connect()) is not None:
+            self.skipTest("not supported on CockroachDB")
+        return f(self)
+
+    return skip_if_crdb_
+
+
 class py3_raises_typeerror(object):
     def __enter__(self):
         pass