diff --git a/Doc/library/asyncore.rst b/Doc/library/asyncore.rst
index 8cdfe200bfe..7edf6128f70 100644
--- a/Doc/library/asyncore.rst
+++ b/Doc/library/asyncore.rst
@@ -209,10 +209,13 @@ any that have been added to the map during asynchronous service) is closed.
    .. method:: accept()
 
       Accept a connection.  The socket must be bound to an address and listening
-      for connections.  The return value is a pair ``(conn, address)`` where
-      *conn* is a *new* socket object usable to send and receive data on the
-      connection, and *address* is the address bound to the socket on the other
-      end of the connection.
+      for connections.  The return value can be either ``None`` or a pair
+      ``(conn, address)`` where *conn* is a *new* socket object usable to send
+      and receive data on the connection, and *address* is the address bound to
+      the socket on the other end of the connection.
+      When ``None`` is returned it means the connection didn't take place, in
+      which case the server should just ignore this event and keep listening
+      for further incoming connections.
 
 
    .. method:: close()
@@ -222,6 +225,12 @@ any that have been added to the map during asynchronous service) is closed.
       flushed).  Sockets are automatically closed when they are
       garbage-collected.
 
+.. class:: dispatcher_with_send()
+
+   A :class:`dispatcher` subclass which adds simple buffered output capability,
+   useful for simple clients. For more sophisticated usage use
+   :class:`asynchat.async_chat`.
+
 .. class:: file_dispatcher()
 
    A file_dispatcher takes a file descriptor or :term:`file object` along
@@ -238,7 +247,7 @@ any that have been added to the map during asynchronous service) is closed.
    socket for use by the :class:`file_dispatcher` class.  Availability: UNIX.
 
 
-.. _asyncore-example:
+.. _asyncore-example-1:
 
 asyncore Example basic HTTP client
 ----------------------------------
@@ -248,7 +257,7 @@ implement its socket handling::
 
    import asyncore, socket
 
-   class http_client(asyncore.dispatcher):
+   class HTTPClient(asyncore.dispatcher):
 
        def __init__(self, host, path):
            asyncore.dispatcher.__init__(self)
@@ -272,6 +281,45 @@ implement its socket handling::
            sent = self.send(self.buffer)
            self.buffer = self.buffer[sent:]
 
-   c = http_client('www.python.org', '/')
 
-   asyncore.loop()
+    client = HTTPClient('www.python.org', '/')
+    asyncore.loop()
+
+.. _asyncore-example-2:
+
+asyncore Example basic echo server
+----------------------------------
+
+Here is abasic echo server that uses the :class:`dispatcher` class to accept
+connections and dispatches the incoming connections to a handler::
+
+    import asyncore
+    import socket
+
+    class EchoHandler(asyncore.dispatcher_with_send):
+
+        def handle_read(self):
+            data = self.recv(8192)
+            self.send(data)
+
+    class EchoServer(asyncore.dispatcher):
+
+        def __init__(self, host, port):
+            asyncore.dispatcher.__init__(self)
+            self.create_socket(socket.AF_INET, socket.SOCK_STREAM)
+            self.set_reuse_addr()
+            self.bind((host, port))
+            self.listen(5)
+
+        def handle_accept(self):
+            pair = self.accept()
+            if pair is None:
+                return
+            else:
+                sock, addr = pair
+                print('Incoming connection from %s' % repr(addr))
+                handler = EchoHandler(sock)
+
+    server = EchoServer('localhost', 8080)
+    asyncore.loop()
+
diff --git a/Lib/asyncore.py b/Lib/asyncore.py
index 7f06e43e716..861495ddfce 100644
--- a/Lib/asyncore.py
+++ b/Lib/asyncore.py
@@ -346,12 +346,15 @@ class dispatcher:
         # XXX can return either an address pair or None
         try:
             conn, addr = self.socket.accept()
-            return conn, addr
+        except TypeError:
+            return None
         except socket.error as why:
-            if why.args[0] == EWOULDBLOCK:
-                pass
+            if why.args[0] in (EWOULDBLOCK, ECONNABORTED):
+                return None
             else:
                 raise
+        else:
+            return conn, addr
 
     def send(self, data):
         try:
diff --git a/Lib/smtpd.py b/Lib/smtpd.py
index 57ad0898419..ab3e0e209b0 100755
--- a/Lib/smtpd.py
+++ b/Lib/smtpd.py
@@ -297,22 +297,11 @@ class SMTPServer(asyncore.dispatcher):
                 localaddr, remoteaddr), file=DEBUGSTREAM)
 
     def handle_accept(self):
-        try:
-            conn, addr = self.accept()
-        except TypeError:
-            # sometimes accept() might return None
-            return
-        except socket.error as err:
-            # ECONNABORTED might be thrown
-            if err.args[0] != errno.ECONNABORTED:
-                raise
-            return
-        else:
-            # sometimes addr == None instead of (ip, port)
-            if addr == None:
-                return
-        print('Incoming connection from %s' % repr(addr), file=DEBUGSTREAM)
-        channel = SMTPChannel(self, conn, addr)
+        pair = self.accept()
+        if pair is not None:
+            conn, addr = pair
+            print('Incoming connection from %s' % repr(addr), file=DEBUGSTREAM)
+            channel = SMTPChannel(self, conn, addr)
 
     # API for "doing something useful with the message"
     def process_message(self, peer, mailfrom, rcpttos, data):
diff --git a/Misc/NEWS b/Misc/NEWS
index b7336256e40..d690318652f 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -143,6 +143,9 @@ C-API
 Library
 -------
 
+- Issue 6706: asyncore accept() method no longer raises EWOULDBLOCK/ECONNABORTED
+  on incomplete connection attempt but returns None instead.
+
 - Issue #10266: uu.decode didn't close in_file explicitly when it was given
   as a filename.  Patch by Brian Brazil.