diff --git a/tests/test_async.py b/tests/test_async.py
index fbb5809d..18fefc6b 100755
--- a/tests/test_async.py
+++ b/tests/test_async.py
@@ -532,6 +532,11 @@ class AsyncTests(ConnectingTestCase):
         else:
             self.fail("No notification received")
 
+    def test_close(self):
+        self.conn.close()
+        self.assertTrue(self.conn.closed)
+        self.assertTrue(self.conn.async_)
+
 
 def test_suite():
     return unittest.TestLoader().loadTestsFromName(__name__)
diff --git a/tests/test_cancel.py b/tests/test_cancel.py
index 4c60c0b7..7068ba54 100755
--- a/tests/test_cancel.py
+++ b/tests/test_cancel.py
@@ -34,12 +34,16 @@ from psycopg2 import extras
 from .testconfig import dsn
 import unittest
 from .testutils import ConnectingTestCase, skip_before_postgres, slow
+from .testutils import crdb_version
 
 
 class CancelTests(ConnectingTestCase):
 
     def setUp(self):
         ConnectingTestCase.setUp(self)
+        # here, instead of a decorator, to avoid creating the temp table
+        if crdb_version(self.conn) is not None:
+            self.skipTest("cancel not supported on CockroachDB")
 
         cur = self.conn.cursor()
         cur.execute('''
@@ -106,11 +110,6 @@ class CancelTests(ConnectingTestCase):
         extras.wait_select(async_conn)
         self.assertEqual(cur.fetchall(), [(1, )])
 
-    def test_async_connection_cancel(self):
-        async_conn = psycopg2.connect(dsn, async_=True)
-        async_conn.close()
-        self.assertTrue(async_conn.closed)
-
 
 def test_suite():
     return unittest.TestLoader().loadTestsFromName(__name__)
diff --git a/tests/testutils.py b/tests/testutils.py
index a23457ee..ec53ba34 100644
--- a/tests/testutils.py
+++ b/tests/testutils.py
@@ -409,13 +409,13 @@ def skip_if_windows(cls):
 
 def crdb_version(conn, __crdb_version=[]):
     """
-    Return the CockroachDB version if that's the db testing, else None.
+    Return the CockroachDB version if that's the db being tested, else None.
 
     Return the number as an integer similar to PQserverVersion: return
     v20.1.3 as 200103.
 
-    Assume all the connections are on the same db: return a chached result on
-    following runs.
+    Assume all the connections are on the same db: return a cached result on
+    following calls.
 
     """
     if __crdb_version: