diff --git a/Lib/email/test/test_email.py b/Lib/email/test/test_email.py
index e66a410..daed3b0 100644
--- a/Lib/email/test/test_email.py
+++ b/Lib/email/test/test_email.py
@@ -1438,7 +1438,24 @@
         eq(msg.get_payload().strip(), '+vv8/f7/')
         eq(msg.get_payload(decode=True), bytesdata)
 
-    def test_body_with_encode_noop(self):
+    def test_binary_body_with_encode_7or8bit(self):
+        # Issue 17171.
+        bytesdata = b'\xfa\xfb\xfc\xfd\xfe\xff'
+        msg = MIMEApplication(bytesdata, _encoder=encoders.encode_7or8bit)
+        # 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)
+        self.assertEqual(msg['Content-Transfer-Encoding'], '8bit')
+        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)
+        self.assertEqual(msg2['Content-Transfer-Encoding'], '8bit')
+
+    def test_binary_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.