diff --git a/Doc/library/email.parser.rst b/Doc/library/email.parser.rst
--- a/Doc/library/email.parser.rst
+++ b/Doc/library/email.parser.rst
@@ -94,12 +94,14 @@
 The :class:`Parser` class, imported from the :mod:`email.parser` module,
 provides an API that can be used to parse a message when the complete contents
 of the message are available in a string or file.  The :mod:`email.parser`
-module also provides a second class, called :class:`HeaderParser` which can be
-used if you're only interested in the headers of the message.
-:class:`HeaderParser` can be much faster in these situations, since it does not
-attempt to parse the message body, instead setting the payload to the raw body
-as a string. :class:`HeaderParser` has the same API as the :class:`Parser`
-class.
+module also provides header-only parsers, called :class:`HeaderParser` and
+:class:`BytesHeaderParser`, which can be used if you're only interested in
+the headers of the message.
+:class:`HeaderParser` and :class:`BytesHeaderParser` can be much faster in
+these situations, since they do not attempt to parse the message body,
+instead setting the payload to the raw body as a string.
+They do have the same API as the :class:`Parser` and :class:`BytesParser`
+classes.
 
 
 .. class:: Parser(_class=email.message.Message)
diff --git a/Lib/email/parser.py b/Lib/email/parser.py
--- a/Lib/email/parser.py
+++ b/Lib/email/parser.py
@@ -4,7 +4,7 @@
 
 """A parser of RFC 2822 and MIME email messages."""
 
-__all__ = ['Parser', 'HeaderParser']
+__all__ = ['Parser', 'HeaderParser', 'BytesParser', 'BytesHeaderParser']
 
 import warnings
 from io import StringIO, TextIOWrapper
@@ -114,3 +114,12 @@
         """
         text = text.decode('ASCII', errors='surrogateescape')
         return self.parser.parsestr(text, headersonly)
+
+
+class BytesHeaderParser(BytesParser):
+    def parse(self, fp, headersonly=True):
+        return BytesParser.parse(self, fp, headersonly=True)
+
+    def parsebytes(self, text, headersonly=True):
+        return BytesParser.parsebytes(self, text, headersonly=True)
+
diff --git a/Lib/test/test_email/test_email.py b/Lib/test/test_email/test_email.py
--- a/Lib/test/test_email/test_email.py
+++ b/Lib/test/test_email/test_email.py
@@ -177,6 +177,40 @@
         gen.flatten(msg, False)
         self.assertEqual(out.getvalue(), msgdata)
 
+    def test_message_rfc822_only_fp(self):
+        # Issue 7970: message/rfc822 not in multipart parsed by
+        # HeaderParser caused an exception when flattened.
+        with openfile('msg_46.txt') as fp:
+            msgdata = fp.read()
+        out = StringIO()
+        with openfile('msg_46.txt') as fp:
+            parser = HeaderParser()
+            msg = parser.parse(fp)
+            gen = Generator(out, True, 0)
+            gen.flatten(msg, False)
+        self.assertEqual(out.getvalue(), msgdata)
+
+    def test_byte_message_rfc822_only(self):
+        with openfile('msg_46.txt', 'rb') as fp:
+            msgdata = fp.read()
+        parser = email.parser.BytesHeaderParser()
+        msg = parser.parsebytes(msgdata)
+        out = BytesIO()
+        gen = email.generator.BytesGenerator(out)
+        gen.flatten(msg)
+        self.assertEqual(out.getvalue(), msgdata)
+
+    def test_byte_message_rfc822_only_fp(self):
+        with openfile('msg_46.txt', 'rb') as fp:
+            msgdata = fp.read()
+        out = BytesIO()
+        with openfile('msg_46.txt', 'rb') as fp:
+            parser = email.parser.BytesHeaderParser()
+            msg = parser.parse(fp)
+            gen = email.generator.BytesGenerator(out)
+            gen.flatten(msg)
+        self.assertEqual(out.getvalue(), msgdata)
+
     def test_get_decoded_payload(self):
         eq = self.assertEqual
         msg = self._msgobj('msg_10.txt')