diff --git a/Lib/test/test_io.py b/Lib/test/test_io.py
index 9b18b70..d0608e3 100644
--- a/Lib/test/test_io.py
+++ b/Lib/test/test_io.py
@@ -798,14 +798,17 @@
         # Inject some None's in there to simulate EWOULDBLOCK
         rawio = self.MockRawIO((b"abc", b"d", None, b"efg", None, None, None))
         bufio = self.tp(rawio)
-
         self.assertEqual(b"abcd", bufio.read(6))
         self.assertEqual(b"e", bufio.read(1))
         self.assertEqual(b"fg", bufio.read())
         self.assertEqual(b"", bufio.peek(1))
-        self.assertTrue(None is bufio.read())
+        self.assertIsNone(bufio.read())
         self.assertEqual(b"", bufio.read())
 
+        rawio = self.MockRawIO((b"a", None, None))
+        self.assertEqual(b"a", rawio.readall())
+        self.assertIsNone(rawio.readall())
+
     def test_read_past_eof(self):
         rawio = self.MockRawIO((b"abc", b"d", b"efg"))
         bufio = self.tp(rawio)