diff --git a/Doc/library/smtplib.rst b/Doc/library/smtplib.rst
index 18560c129f7..4f3b572aab4 100644
--- a/Doc/library/smtplib.rst
+++ b/Doc/library/smtplib.rst
@@ -24,12 +24,15 @@ Protocol) and :rfc:`1869` (SMTP Service Extensions).
 
    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
-   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).
+   host and port parameters are given, the SMTP :meth:`connect` method is
+   called 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 global default timeout
+   setting will be used).
 
    For normal use, you should only require the initialization/connect,
    :meth:`sendmail`, and :meth:`~smtplib.quit` methods.
@@ -45,12 +48,13 @@ Protocol) and :rfc:`1869` (SMTP Service Extensions).
    :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 omitted, the standard SMTP-over-SSL port (465) is used. *keyfile*
-   and *certfile* are also optional, and can contain a PEM formatted private key
-   and certificate chain file for the SSL connection. 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).
+   *port* is omitted, the standard SMTP-over-SSL port (465) is used.
+   *local_hostname* has the same meaning as it does for 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. 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).
 
    .. versionadded:: 2.6
 
@@ -58,13 +62,15 @@ Protocol) and :rfc:`1869` (SMTP Service Extensions).
 .. class:: LMTP([host[, port[, local_hostname]]])
 
    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. To specify a
-   Unix socket, you must use an absolute path for *host*, starting with a '/'.
+   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.  *local_hostname* has the same meaning as it does for 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
-   socket, LMTP generally don't support or require any authentication, but your
-   mileage might vary.
+   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.
 
    .. versionadded:: 2.6
 
diff --git a/Lib/smtplib.py b/Lib/smtplib.py
index a3213b33d71..7f07840044b 100755
--- a/Lib/smtplib.py
+++ b/Lib/smtplib.py
@@ -238,10 +238,11 @@ class SMTP:
         If specified, `host' is the name of the remote host to which to
         connect.  If specified, `port' specifies the port to which to connect.
         By default, smtplib.SMTP_PORT is used.  If a host is specified the
-        connect method is called, and if it returns anything other than
-        a success code an SMTPConnectError is raised.  If specified,
-        `local_hostname` is used as the FQDN of the local host.  By default,
-        the local hostname is found using socket.getfqdn().
+        connect method is called, and if it returns anything other than a
+        success code an SMTPConnectError is raised.  If specified,
+        `local_hostname` is used as the FQDN of the local host for the
+        HELO/EHLO command.  Otherwise, the local hostname is found using
+        socket.getfqdn().
 
         """
         self.timeout = timeout
@@ -759,12 +760,15 @@ class SMTP:
 if _have_ssl:
 
     class SMTP_SSL(SMTP):
-        """ This is a subclass derived from SMTP that connects over an SSL encrypted
-        socket (to use this class you need a socket module that was compiled with SSL
-        support). If host is not specified, '' (the local host) is used. If port is
-        omitted, the standard SMTP-over-SSL port (465) is used. keyfile and certfile
-        are also optional - they can contain a PEM formatted private key and
-        certificate chain file for the SSL connection.
+        """ This is a subclass derived from SMTP that connects over an SSL
+        encrypted socket (to use this class you need a socket module that was
+        compiled with SSL support). If host is not specified, '' (the local
+        host) is used. If port is omitted, the standard SMTP-over-SSL port
+        (465) is used.  local_hostname has the same meaning as it does in the
+        SMTP class.  keyfile and certfile are also optional - they can contain
+        a PEM formatted private key and certificate chain file for the SSL
+        connection.
+
         """
 
         default_port = SMTP_SSL_PORT
@@ -795,9 +799,10 @@ class LMTP(SMTP):
     """LMTP - Local Mail Transfer Protocol
 
     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 connect() method must support that as well as a regular
-    host:port server. To specify a Unix socket, you must use an absolute
+    on the standard SMTP client. It's common to use Unix sockets for
+    LMTP, so our connect() method must support that as well as a regular
+    host:port server.  local_hostname has the same meaning as it does in
+    the SMTP class.  To specify a Unix socket, you must use an absolute
     path as the host, starting with a '/'.
 
     Authentication is supported, using the regular SMTP mechanism. When