diff --git a/Doc/library/email.generator.rst b/Doc/library/email.generator.rst
index 22d8b09..85b32fe 100644
--- a/Doc/library/email.generator.rst
+++ b/Doc/library/email.generator.rst
@@ -79,8 +79,8 @@
 
       Messages parsed with a Bytes parser that have a
       :mailheader:`Content-Transfer-Encoding` of 8bit will be converted to a
-      use a 7bit Content-Transfer-Encoding.  Any other non-ASCII bytes in the
-      message structure will be converted to '?' characters.
+      use a 7bit Content-Transfer-Encoding.  Non-ASCII bytes in the headers
+      will be :rfc:`2047` encoded with a charset of `unknown-8bit`.
 
       .. versionchanged:: 3.2
          Added support for re-encoding 8bit message bodies, and the *linesep*
diff --git a/Doc/library/email.header.rst b/Doc/library/email.header.rst
index ff2b484..29752c4 100644
--- a/Doc/library/email.header.rst
+++ b/Doc/library/email.header.rst
@@ -130,8 +130,14 @@
 
    .. method:: __str__()
 
-      A helper for :class:`str`'s :func:`encode` method.  Returns the header as
-      a Unicode string.
+      Returns an approximation of the :class:`Header` as a string, using an
+      unlimited line length.  All pieces are converted to unicode using the
+      specified encoding and joined together appropriately.  Any pieces with a
+      charset of `unknown-8bit` are decoded as `ASCII` using the `replace`
+      error handler.
+
+      .. versionchanged:: 3.2
+         Added handling for the `unknown-8bit` charset.
 
 
    .. method:: __eq__(other)
diff --git a/Doc/library/email.message.rst b/Doc/library/email.message.rst
index e76e689..29f7ba3 100644
--- a/Doc/library/email.message.rst
+++ b/Doc/library/email.message.rst
@@ -169,9 +169,10 @@
    Note that in all cases, any envelope header present in the message is not
    included in the mapping interface.
 
-   In a model generated from bytes, any header values that (in contravention
-   of the RFCs) contain non-ASCII bytes will have those bytes transformed
-   into '?' characters when the values are retrieved through this interface.
+   In a model generated from bytes, any header values that (in contravention of
+   the RFCs) contain non-ASCII bytes will, when retrieved through this
+   interface, be represented as :class:`~email.header.Header` objects with
+   a charset of `unknown-8bit`.
 
 
    .. method:: __len__()
diff --git a/Doc/whatsnew/3.2.rst b/Doc/whatsnew/3.2.rst
index b6e2550..69b318e 100644
--- a/Doc/whatsnew/3.2.rst
+++ b/Doc/whatsnew/3.2.rst
@@ -618,6 +618,8 @@
 * Given bytes input to the model, :class:`~email.generator.Generator` will
   convert message bodies that have a :mailheader:`Content-Transfer-Encoding` of
   *8bit* to instead have a *7bit* :mailheader:`Content-Transfer-Encoding`.
+  XXX: Headers with Un-encoded non-ASCII bytes will be :rfc:`2047`\ -encoded
+  using the charset `unknown-8bit`.
 
 * A new class :class:`~email.generator.BytesGenerator` produces bytes as output,
   preserving any unchanged non-ASCII data that was present in the input used to
diff --git a/Lib/email/charset.py b/Lib/email/charset.py
index 898beed..8591527 100644
--- a/Lib/email/charset.py
+++ b/Lib/email/charset.py
@@ -28,6 +28,7 @@
 RFC2047_CHROME_LEN = 7
 
 DEFAULT_CHARSET = 'us-ascii'
+UNKNOWN8BIT = 'unknown-8bit'
 EMPTYSTRING = ''
 
 
@@ -153,6 +154,16 @@
 
 
 
+# Convenience function for encoding strings, taking into account
+# that they might be unknown-8bit (ie: have surrogate-escaped bytes)
+def _encode(string, codec):
+    if codec == UNKNOWN8BIT:
+        return string.encode('ascii', 'surrogateescape')
+    else:
+        return string.encode(codec)
+
+
+
 class Charset:
     """Map character sets to their email properties.
 
@@ -282,8 +293,7 @@
         :return: The encoded string, with RFC 2047 chrome.
         """
         codec = self.output_codec or 'us-ascii'
-        charset = self.get_output_charset()
-        header_bytes = string.encode(codec)
+        header_bytes = _encode(string, codec)
         # 7bit/8bit encodings return the string unchanged (modulo conversions)
         encoder_module = self._get_encoder(header_bytes)
         if encoder_module is None:
@@ -309,7 +319,7 @@
         """
         # See which encoding we should use.
         codec = self.output_codec or 'us-ascii'
-        header_bytes = string.encode(codec)
+        header_bytes = _encode(string, codec)
         encoder_module = self._get_encoder(header_bytes)
         encoder = partial(encoder_module.header_encode, charset=str(self))
         # Calculate the number of characters that the RFC 2047 chrome will
@@ -333,7 +343,7 @@
         for character in string:
             current_line.append(character)
             this_line = EMPTYSTRING.join(current_line)
-            length = encoder_module.header_length(this_line.encode(charset))
+            length = encoder_module.header_length(_encode(this_line, charset))
             if length > maxlen:
                 # This last character doesn't fit so pop it off.
                 current_line.pop()
@@ -343,12 +353,12 @@
                 else:
                     separator = (' ' if lines else '')
                     joined_line = EMPTYSTRING.join(current_line)
-                    header_bytes = joined_line.encode(codec)
+                    header_bytes = _encode(joined_line, codec)
                     lines.append(encoder(header_bytes))
                 current_line = [character]
                 maxlen = next(maxlengths) - extra
         joined_line = EMPTYSTRING.join(current_line)
-        header_bytes = joined_line.encode(codec)
+        header_bytes = _encode(joined_line, codec)
         lines.append(encoder(header_bytes))
         return lines
 
diff --git a/Lib/email/header.py b/Lib/email/header.py
index d462bf0..f90883f 100644
--- a/Lib/email/header.py
+++ b/Lib/email/header.py
@@ -17,7 +17,8 @@
 import email.base64mime
 
 from email.errors import HeaderParseError
-from email.charset import Charset
+from email import charset as _charset
+Charset = _charset.Charset
 
 NL = '\n'
 SPACE = ' '
@@ -210,6 +211,9 @@
             # from a charset to None/us-ascii, or from None/us-ascii to a
             # charset.  Only do this for the second and subsequent chunks.
             nextcs = charset
+            if nextcs == _charset.UNKNOWN8BIT:
+                original_bytes = string.encode('ascii', 'surrogateescape')
+                string = original_bytes.decode('ascii', 'replace')
             if uchunks:
                 if lastcs not in (None, 'us-ascii'):
                     if nextcs in (None, 'us-ascii'):
@@ -263,7 +267,8 @@
         # Ensure that the bytes we're storing can be decoded to the output
         # character set, otherwise an early error is thrown.
         output_charset = charset.output_codec or 'us-ascii'
-        s.encode(output_charset, errors)
+        if output_charset != _charset.UNKNOWN8BIT:
+            s.encode(output_charset, errors)
         self._chunks.append((s, charset))
 
     def encode(self, splitchars=';, \t', maxlinelen=None, linesep='\n'):
diff --git a/Lib/email/message.py b/Lib/email/message.py
index d2483ca..b821bfd 100644
--- a/Lib/email/message.py
+++ b/Lib/email/message.py
@@ -16,7 +16,9 @@
 # Intrapackage imports
 from email import utils
 from email import errors
-from email.charset import Charset
+from email import header
+from email import charset as _charset
+Charset = _charset.Charset
 
 SEMISPACE = '; '
 
@@ -31,16 +33,15 @@
 
 
 # Helper functions
-def _sanitize_surrogates(value):
-    # If the value contains surrogates, re-decode and replace the original
-    # non-ascii bytes with '?'s.  Used to sanitize header values before letting
-    # them escape as strings.
+def _sanitize_header(name, value):
+    # If the header value contains surrogates, return a Header using
+    # the unknown-8bit charset to encode the bytes as encoded words.
     if not isinstance(value, str):
-        # Header object
+        # Assume it is already a header object
         return value
     if _has_surrogates(value):
-        original_bytes = value.encode('ascii', 'surrogateescape')
-        return original_bytes.decode('ascii', 'replace').replace('\ufffd', '?')
+        return header.Header(value, charset=_charset.UNKNOWN8BIT,
+                             header_name=name)
     else:
         return value
 
@@ -398,7 +399,7 @@
         Any fields deleted and re-inserted are always appended to the header
         list.
         """
-        return [_sanitize_surrogates(v) for k, v in self._headers]
+        return [_sanitize_header(k, v) for k, v in self._headers]
 
     def items(self):
         """Get all the message's header fields and values.
@@ -408,7 +409,7 @@
         Any fields deleted and re-inserted are always appended to the header
         list.
         """
-        return [(k, _sanitize_surrogates(v)) for k, v in self._headers]
+        return [(k, _sanitize_header(k, v)) for k, v in self._headers]
 
     def get(self, name, failobj=None):
         """Get a header value.
@@ -419,7 +420,7 @@
         name = name.lower()
         for k, v in self._headers:
             if k.lower() == name:
-                return _sanitize_surrogates(v)
+                return _sanitize_header(k, v)
         return failobj
 
     #
@@ -439,7 +440,7 @@
         name = name.lower()
         for k, v in self._headers:
             if k.lower() == name:
-                values.append(_sanitize_surrogates(v))
+                values.append(_sanitize_header(k, v))
         if not values:
             return failobj
         return values
diff --git a/Lib/email/test/test_email.py b/Lib/email/test/test_email.py
index 4855371..a1798ce 100644
--- a/Lib/email/test/test_email.py
+++ b/Lib/email/test/test_email.py
@@ -2841,7 +2841,7 @@
                                      cte='8bit',
                                      bodyline='pöstal').encode('utf-8')
         msg = email.message_from_bytes(m)
-        self.assertEqual(msg.get_payload(), "p��stal\n")
+        self.assertEqual(msg.get_payload(), "p\uFFFD\uFFFDstal\n")
         self.assertEqual(msg.get_payload(decode=True),
                          "pöstal\n".encode('utf-8'))
 
@@ -2874,7 +2874,7 @@
                                      cte='quoted-printable',
                                      bodyline='p=C3=B6stál').encode('utf-8')
         msg = email.message_from_bytes(m)
-        self.assertEqual(msg.get_payload(), 'p=C3=B6st��l\n')
+        self.assertEqual(msg.get_payload(), 'p=C3=B6st\uFFFD\uFFFDl\n')
         self.assertEqual(msg.get_payload(decode=True),
                         'pöstál\n'.encode('utf-8'))
 
@@ -2899,52 +2899,65 @@
                          '<,.V<W1A; á \n'.encode('utf-8'))
 
 
-    headertest_msg = textwrap.dedent("""\
-        From: foo@bar.com
-        To: báz
-        Subject: Maintenant je vous présente mon collègue, le pouf célèbre
-        \tJean de Baddie
-        From: göst
-
-        Yes, they are flying.
-        """).encode('utf-8')
+    headertest_headers = (
+        ('From: foo@bar.com', ('From', 'foo@bar.com')),
+        ('To: báz', ('To', '=?unknown-8bit?q?b=C3=A1z?=')),
+        ('Subject: Maintenant je vous présente mon collègue, le pouf célèbre\n'
+            '\tJean de Baddie',
+            ('Subject', '=?unknown-8bit?q?Maintenant_je_vous_pr=C3=A9sente_mon_'
+                'coll=C3=A8gue=2C_le_pouf_c=C3=A9l=C3=A8bre?=\n'
+                ' =?unknown-8bit?q?_Jean_de_Baddie?=')),
+        ('From: göst', ('From', '=?unknown-8bit?b?Z8O2c3Q=?=')),
+        )
+    headertest_msg = ('\n'.join([src for (src, _) in headertest_headers]) +
+        '\nYes, they are flying.\n').encode('utf-8')
 
     def test_get_8bit_header(self):
         msg = email.message_from_bytes(self.headertest_msg)
-        self.assertEqual(msg.get('to'), 'b??z')
-        self.assertEqual(msg['to'], 'b??z')
+        self.assertEqual(str(msg.get('to')), 'b\uFFFD\uFFFDz')
+        self.assertEqual(str(msg['to']), 'b\uFFFD\uFFFDz')
 
     def test_print_8bit_headers(self):
         msg = email.message_from_bytes(self.headertest_msg)
         self.assertEqual(str(msg),
-                         self.headertest_msg.decode(
-                            'ascii', 'replace').replace('�', '?'))
+                         textwrap.dedent("""\
+                            From: {}
+                            To: {}
+                            Subject: {}
+                            From: {}
+
+                            Yes, they are flying.
+                            """).format(*[expected[1] for (_, expected) in
+                                        self.headertest_headers]))
 
     def test_values_with_8bit_headers(self):
         msg = email.message_from_bytes(self.headertest_msg)
-        self.assertListEqual(msg.values(),
+        self.assertListEqual([str(x) for x in msg.values()],
                               ['foo@bar.com',
-                               'b??z',
-                               'Maintenant je vous pr??sente mon '
-                                   'coll??gue, le pouf c??l??bre\n'
+                               'b\uFFFD\uFFFDz',
+                               'Maintenant je vous pr\uFFFD\uFFFDsente mon '
+                                   'coll\uFFFD\uFFFDgue, le pouf '
+                                   'c\uFFFD\uFFFDl\uFFFD\uFFFDbre\n'
                                    '\tJean de Baddie',
-                               "g??st"])
+                               "g\uFFFD\uFFFDst"])
 
     def test_items_with_8bit_headers(self):
         msg = email.message_from_bytes(self.headertest_msg)
-        self.assertListEqual(msg.items(),
+        self.assertListEqual([(str(x), str(y)) for (x, y) in msg.items()],
                               [('From', 'foo@bar.com'),
-                               ('To', 'b??z'),
-                               ('Subject', 'Maintenant je vous pr??sente mon '
-                                              'coll??gue, le pouf c??l??bre\n'
-                                              '\tJean de Baddie'),
-                               ('From', 'g??st')])
+                               ('To', 'b\uFFFD\uFFFDz'),
+                               ('Subject', 'Maintenant je vous '
+                                  'pr\uFFFD\uFFFDsente '
+                                  'mon coll\uFFFD\uFFFDgue, le pouf '
+                                  'c\uFFFD\uFFFDl\uFFFD\uFFFDbre\n'
+                                  '\tJean de Baddie'),
+                               ('From', 'g\uFFFD\uFFFDst')])
 
     def test_get_all_with_8bit_headers(self):
         msg = email.message_from_bytes(self.headertest_msg)
-        self.assertListEqual(msg.get_all('from'),
+        self.assertListEqual([str(x) for x in msg.get_all('from')],
                               ['foo@bar.com',
-                               'g??st'])
+                               'g\uFFFD\uFFFDst'])
 
     non_latin_bin_msg = textwrap.dedent("""\
         From: foo@bar.com
@@ -2964,13 +2977,12 @@
         email.generator.BytesGenerator(out).flatten(msg)
         self.assertEqual(out.getvalue(), self.non_latin_bin_msg)
 
-    # XXX: ultimately the '?' should turn into CTE encoded bytes
-    # using 'unknown-8bit' charset.
-    non_latin_bin_msg_as7bit = textwrap.dedent("""\
+    non_latin_bin_msg_as7bit_wrapped = textwrap.dedent("""\
         From: foo@bar.com
-        To: b??z
-        Subject: Maintenant je vous pr??sente mon coll??gue, le pouf c??l??bre
-        \tJean de Baddie
+        To: =?unknown-8bit?q?b=C3=A1z?=
+        Subject: =?unknown-8bit?q?Maintenant_je_vous_pr=C3=A9sente_mon_coll=C3=A8gue?=
+         =?unknown-8bit?q?=2C_le_pouf_c=C3=A9l=C3=A8bre?=
+         =?unknown-8bit?q?_Jean_de_Baddie?=
         Mime-Version: 1.0
         Content-Type: text/plain; charset="utf-8"
         Content-Transfer-Encoding: base64
@@ -2982,7 +2994,7 @@
         msg = email.message_from_bytes(self.non_latin_bin_msg)
         out = StringIO()
         email.generator.Generator(out).flatten(msg)
-        self.assertEqual(out.getvalue(), self.non_latin_bin_msg_as7bit)
+        self.assertEqual(out.getvalue(), self.non_latin_bin_msg_as7bit_wrapped)
 
     def test_bytes_generator_with_unix_from(self):
         # The unixfrom contains a current date, so we can't check it
@@ -2995,6 +3007,12 @@
         self.assertEqual(lines[0].split()[0], b'From')
         self.assertEqual(b'\n'.join(lines[1:]), self.non_latin_bin_msg)
 
+    non_latin_bin_msg_as7bit = non_latin_bin_msg_as7bit_wrapped.split('\n')
+    non_latin_bin_msg_as7bit[2:4] = [
+        'Subject: =?unknown-8bit?q?Maintenant_je_vous_pr=C3=A9sente_mon_'
+         'coll=C3=A8gue=2C_le_pouf_c=C3=A9l=C3=A8bre?=']
+    non_latin_bin_msg_as7bit = '\n'.join(non_latin_bin_msg_as7bit)
+
     def test_message_from_binary_file(self):
         fn = 'test.msg'
         self.addCleanup(unlink, fn)
diff --git a/Misc/NEWS b/Misc/NEWS
index 5361574..8c7c7fd 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -40,6 +40,10 @@
 Library
 -------
 
+- Issue #10686: the email package now :rfc:`2047`\ -encodes headers with
+  non-ASCII bytes (parsed by a Bytes Parser) when doing conversion to
+  7bit-clean presentation, instead of replacing them with ?s.
+
 - email.header.Header was incorrectly encoding folding white space when
   rfc2047-encoding header values with embedded newlines, leaving them
   without folding whitespace.  It now uses the continuation_ws, as it