diff --git a/Doc/library/smtplib.rst b/Doc/library/smtplib.rst
--- a/Doc/library/smtplib.rst
+++ b/Doc/library/smtplib.rst
@@ -20,17 +20,19 @@ details of SMTP and ESMTP operation, con
 Protocol) and :rfc:`1869` (SMTP Service Extensions).
 
 
 .. class:: SMTP(host='', port=0, local_hostname=None[, timeout], source_address=None)
 
    A :class:`SMTP` instance encapsulates an SMTP connection.  It has methods
    that support a full repertoire of SMTP and ESMTP operations. If the optional
    host and port parameters are given, the SMTP :meth:`connect` method is called
-   with those parameters during initialization.  If the :meth:`connect` call
+   with those parameters during initialization.  If specified, *local_hostname* is
+   used as the FQDN of the local host.  By default, the local hostname is found
+   using :func:`socket.getfqdn`.  If the :meth:`connect` call
    returns anything other than a success code, an :exc:`SMTPConnectError` is
    raised. The optional *timeout* parameter specifies a timeout in seconds for
    blocking operations like the connection attempt (if not specified, the
    global default timeout setting will be used). The optional source_address
    parameter allows to bind to some specific source address in a machine with
    multiple network interfaces, and/or to some specific source TCP port. It
    takes a 2-tuple (host, port), for the socket to bind to as its source
    address before connecting. If omitted (or if host or port are ``''`` and/or
@@ -52,23 +54,26 @@ Protocol) and :rfc:`1869` (SMTP Service 
     >>>
 
    .. versionchanged:: 3.3
       Support for the :keyword:`with` statement was added.
 
    .. versionchanged:: 3.3
       source_address argument was added.
 
-.. class:: SMTP_SSL(host='', port=0, local_hostname=None, keyfile=None, certfile=None[, timeout], context=None, source_address=None)
+.. class:: SMTP_SSL(host='', port=0, local_hostname=None, keyfile=None, certfile=None \
+                    [, timeout], context=None, source_address=None)
 
    A :class:`SMTP_SSL` instance behaves exactly the same as instances of
    :class:`SMTP`. :class:`SMTP_SSL` should be used for situations where SSL is
    required from the beginning of the connection and using :meth:`starttls` is
    not appropriate. If *host* is not specified, the local host is used. If
-   *port* is zero, the standard SMTP-over-SSL port (465) is used. *keyfile*
+   *port* is zero, the standard SMTP-over-SSL port (465) is used.  If specified,
+   *local_hostname* is used as the FQDN of the local host.  By default, the
+   local hostname is found using :func:`socket.getfqdn`.  *keyfile*
    and *certfile* are also optional, and can contain a PEM formatted private key
    and certificate chain file for the SSL connection. *context* also optional, can contain
    a SSLContext, and is an alternative to keyfile and certfile; If it is specified both
    keyfile and certfile must be None.  The optional *timeout*
    parameter specifies a timeout in seconds for blocking operations like the
    connection attempt (if not specified, the global default timeout setting
    will be used). The optional source_address parameter allows to bind to some
    specific source address in a machine with multiple network interfaces,
@@ -86,17 +91,19 @@ Protocol) and :rfc:`1869` (SMTP Service 
 
 .. class:: LMTP(host='', port=LMTP_PORT, local_hostname=None, source_address=None)
 
    The LMTP protocol, which is very similar to ESMTP, is heavily based on the
    standard SMTP client. It's common to use Unix sockets for LMTP, so our
    :meth:`connect` method must support that as well as a regular host:port
    server. The optional arguments local_hostname and source_address have the
    same meaning as that of SMTP client. To specify a Unix socket, you must use
-   an absolute path for *host*, starting with a '/'.
+   an absolute path for *host*, starting with a '/'. If specified, *local_hostname*
+   is used as the FQDN of the local host.  By default, the local hostname is found
+   using :func:`socket.getfqdn`.
 
    Authentication is supported, using the regular SMTP mechanism. When using a Unix
    socket, LMTP generally don't support or require any authentication, but your
    mileage might vary.
 
 
 A nice selection of exceptions is defined as well: