diff --git a/Doc/library/socket.rst b/Doc/library/socket.rst
index 0a0f76420b3..c5f2b7c5226 100644
--- a/Doc/library/socket.rst
+++ b/Doc/library/socket.rst
@@ -552,6 +552,12 @@ correspond to Unix system calls applicable to sockets.
    remote end will receive no more data (after queued data is flushed). Sockets are
    automatically closed when they are garbage-collected.
 
+   .. note::
+      :meth:`close()` releases the resource associated with a connection but
+      does not necessarily close the connection immediately.  If you want
+      to close the connection in a timely fashion, call :meth:`shutdown()`
+      before :meth:`close()`.
+
 
 .. method:: socket.connect(address)