diff --git a/Doc/library/smtplib.rst b/Doc/library/smtplib.rst
index c5f8516f768a68..6f6262fd05c69a 100644
--- a/Doc/library/smtplib.rst
+++ b/Doc/library/smtplib.rst
@@ -24,10 +24,12 @@ Protocol) and :rfc:`1869` (SMTP Service Extensions).
 .. class:: SMTP(host='', port=0, local_hostname=None[, timeout], source_address=None)
 
    An :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 specified,
-   *local_hostname* is used as the FQDN of the local host in the HELO/EHLO
+   that support a full repertoire of SMTP and ESMTP operations.
+   If *host* is omitted or set to an empty string, no connection is made during initialization; you must
+   call :meth:`connect` manually before using the instance.
+   If *port* is zero,the value of the :attr:`default_port` attribute is used.
+
+   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
@@ -81,9 +83,13 @@ Protocol) and :rfc:`1869` (SMTP Service Extensions).
    An :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.  The optional
-   arguments *local_hostname*, *timeout* and *source_address* have the same
+   not appropriate. If the optional *host* and *port* parameters are given, the
+   SMTP_SSL :meth:`connect` method is called with those parameters during initialization.
+   If *host* is omitted or an empty string, no connection is made during initialization;
+   you must call :meth:`connect` manually before using the instance. If
+   *port* is zero, the standard SMTP-over-SSL port (465) is used.
+
+   The optional arguments *local_hostname*, *timeout* and *source_address* have the same
    meaning as they do in the :class:`SMTP` class.  *context*, also optional,
    can contain a :class:`~ssl.SSLContext` and allows configuring various
    aspects of the secure connection.  Please read :ref:`ssl-security` for