diff --git a/Doc/library/socket.rst b/Doc/library/socket.rst
--- a/Doc/library/socket.rst
+++ b/Doc/library/socket.rst
@@ -394,13 +394,8 @@
    Return a string containing the hostname of the machine where  the Python
    interpreter is currently executing.
 
-   If you want to know the current machine's IP address, you may want to use
-   ``gethostbyname(gethostname())``. This operation assumes that there is a
-   valid address-to-host mapping for the host, and the assumption does not
-   always hold.
-
    Note: :func:`gethostname` doesn't always return the fully qualified domain
-   name; use ``getfqdn()`` (see above).
+   name; use :func:`getfqdn()`.
 
 
 .. function:: gethostbyaddr(ip_address)