diff --git a/Lib/email/test/test_email.py b/Lib/email/test/test_email.py
index 2fa4aa8..e66a410 100644
--- a/Lib/email/test/test_email.py
+++ b/Lib/email/test/test_email.py
@@ -1438,6 +1438,22 @@
         eq(msg.get_payload().strip(), '+vv8/f7/')
         eq(msg.get_payload(decode=True), bytesdata)
 
+    def test_body_with_encode_noop(self):
+        # Issue 16564: This does not produce an RFC valid message, since to be
+        # valid it should have a CTE of binary.  But the below works in
+        # Python2, and is documented as working this way.
+        bytesdata = b'\xfa\xfb\xfc\xfd\xfe\xff'
+        msg = MIMEApplication(bytesdata, _encoder=encoders.encode_noop)
+        # Treated as a string, this will be invalid code points.
+        self.assertEqual(msg.get_payload(), '\uFFFD' * len(bytesdata))
+        self.assertEqual(msg.get_payload(decode=True), bytesdata)
+        s = BytesIO()
+        g = BytesGenerator(s)
+        g.flatten(msg)
+        wireform = s.getvalue()
+        msg2 = email.message_from_bytes(wireform)
+        self.assertEqual(msg.get_payload(), '\uFFFD' * len(bytesdata))
+        self.assertEqual(msg2.get_payload(decode=True), bytesdata)
 
 
 # Test the basic MIMEText class