diff --git a/Doc/library/smtplib.rst b/Doc/library/smtplib.rst
index 9593dea..9f67028 100644
--- a/Doc/library/smtplib.rst
+++ b/Doc/library/smtplib.rst
@@ -25,7 +25,10 @@
    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 in the HELO/EHLO command.  Otherwise, 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
@@ -57,13 +60,17 @@
    .. 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.  The optional
+   arguments *local_hostname* and *source_address* have the same meaning as
+   they do in the :class:`SMTP` class.  *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
@@ -90,7 +97,7 @@
    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
+   same meaning as they do in the :class:`SMTP` class. To specify a Unix socket, you must use
    an absolute path for *host*, starting with a '/'.
 
    Authentication is supported, using the regular SMTP mechanism. When using a Unix