diff --git a/Lib/email/encoders.py b/Lib/email/encoders.py
--- a/Lib/email/encoders.py
+++ b/Lib/email/encoders.py
@@ -76,3 +76,9 @@
 
 def encode_noop(msg):
     """Do nothing."""
+    # Well, not quite *nothing*: in Python3 we have to turn bytes into a string
+    # in our internal surrogateescaped form in order to keep the model
+    # consistent.
+    orig = msg.get_payload()
+    if not isinstance(orig, str):
+        msg.set_payload(orig.decode('ascii', 'surrogateescape'))
diff --git a/Lib/email/generator.py b/Lib/email/generator.py
--- a/Lib/email/generator.py
+++ b/Lib/email/generator.py
@@ -397,6 +397,9 @@
         else:
             super(BytesGenerator,self)._handle_text(msg)
 
+    # Default body handler
+    _writeBody = _handle_text
+
     @classmethod
     def _compile_re(cls, s, flags):
         return re.compile(s.encode('ascii'), flags)
diff --git a/Lib/email/test/test_email.py b/Lib/email/test/test_email.py
--- 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