diff --git a/Doc/includes/email-mime.py b/Doc/includes/email-mime.py
index f64df83..8ddd486 100644
--- a/Doc/includes/email-mime.py
+++ b/Doc/includes/email-mime.py
@@ -27,5 +27,5 @@
 
 # Send the email via our own SMTP server.
 s = smtplib.SMTP()
-s.sendmail(me, family, msg.as_string())
+s.sendmail(msg)
 s.quit()
diff --git a/Doc/includes/email-simple.py b/Doc/includes/email-simple.py
index 689511e..b069ab0 100644
--- a/Doc/includes/email-simple.py
+++ b/Doc/includes/email-simple.py
@@ -17,8 +17,7 @@
 msg['From'] = me
 msg['To'] = you
 
-# Send the message via our own SMTP server, but don't include the
-# envelope header.
+# Send the message via our own SMTP server.
 s = smtplib.SMTP()
-s.sendmail(me, [you], msg.as_string())
+s.sendmail(msg)
 s.quit()
diff --git a/Doc/library/smtplib.rst b/Doc/library/smtplib.rst
index 0c65290..858301d 100644
--- a/Doc/library/smtplib.rst
+++ b/Doc/library/smtplib.rst
@@ -274,9 +274,14 @@
    .. note::
 
       The *from_addr* and *to_addrs* parameters are used to construct the message
-      envelope used by the transport agents. The :class:`SMTP` does not modify the
+      envelope used by the transport agents.  ``sendmail`` does not modify the
       message headers in any way.
 
+   msg may be a string containing characters in the ASCII range, or a byte
+   string.  A string is encoded to bytes using the ascii codec, and lone ``\r``
+   and ``\n`` characters are converted to ``\r\n`` characters.  A byte string
+   is not modified.
+
    If there has been no previous ``EHLO`` or ``HELO`` command this session, this
    method tries ESMTP ``EHLO`` first. If the server does ESMTP, message size and
    each of the specified options will be passed to it (if the option is in the
@@ -311,6 +316,27 @@
    Unless otherwise noted, the connection will be open even after an exception is
    raised.
 
+   .. versionchanged:: 3.2 *msg* may be a byte string.
+
+
+.. method:: SMTP.send_message(msg, from_addr=None, to_addrs=None, mail_options=[], rcpt_options=[])
+
+   This is a convenience method for calling :meth:`sendmail` with the message
+   represented by an :class:`email.message.Message` object.  The arguments have
+   the same meaning as for :meth:`sendmail`, except that *msg* is a ``Message``
+   object.
+
+   If *from_addr* is ``None``, ``send_message`` sets its value to the value of
+   the :mailheader:`From` header from *msg*.  If *to_addrs* is ``None``,
+   ``send_message`` combines the values (if any) of the :mailheader:`To`,
+   :mailheader:`CC`, and :mailheader:`Bcc` fields from *msg*.  Regardless of
+   the values of *from_addr* and *to_addrs*, ``send_message`` deletes any  Bcc
+   field from *msg*.  It then serializes *msg* using
+   :class:`~email.generator.BytesGenerator` with ``\r\n`` as the *linesep*, and
+   calls :meth:`sendmail` to transmit the resulting message.
+
+   .. versionadded:: 3.2
+
 
 .. method:: SMTP.quit()
 
@@ -366,5 +392,5 @@
 .. note::
 
    In general, you will want to use the :mod:`email` package's features to
-   construct an email message, which you can then convert to a string and send
-   via :meth:`sendmail`; see :ref:`email-examples`.
+   construct an email message, which you can then send
+   via :meth:`~smtplib.SMTP.send_message`; see :ref:`email-examples`.
diff --git a/Doc/whatsnew/3.2.rst b/Doc/whatsnew/3.2.rst
index 87f9e94..613331f 100644
--- a/Doc/whatsnew/3.2.rst
+++ b/Doc/whatsnew/3.2.rst
@@ -540,6 +540,14 @@
 
   (Contributed by Neil Schemenauer and Nick Coghlan; :issue:`5178`.)
 
+* The :mod:`smtplib` :class:`~smtplib.SMTP` class now accepts a byte string
+  for the *msg* argument to the :meth:`~smtplib.SMTP.sendmail` method,
+  and a new method, :meth:`~smtplib.SMTP.send_message` accepts a
+  :class:`~email.message.Message` object and can optionally obtain the
+  *from_addr* and *to_addrs* addresses directly from the object.
+
+  (Contributed by R. David Murray, :issue:`10321`.)
+
 
 Multi-threading
 ===============