Thread limitations and SocketServer?

[sblakey at freei.net]

I am running a SocketServer on a Linux box (/prov/version is 
Linux version 2.2.13 (root at ooc3) (gcc version egcs-2.91.66 19990314/Linux 
(egcs-1.1.2 release)) #2 SMP Wed Dec 29 07:57:42 PST 1999) and am
running into a thread-related problem.

Once this server is hit with a heavy enough load, the following
traceback begins to appear with alarming frequencey:

Traceback (innermost last):
  File "/usr/lib/python1.5/SocketServer.py", line 213, in handle_request
    self.process_request(request, client_address)
  File "/usr/lib/python1.5/SocketServer.py", line 321, in process_request
    (request, client_address))
error: can't start new thread

The offending section of the SocketServer module seems innocuous enough:

    def process_request(self, request, client_address):
        """Start a new thread to process the request."""
        import thread
        thread.start_new_thread(self.finish_request,
                                (request, client_address))

Obviously some internal limitation on the number of concurrent threads
is being reached.  My question is: is this problwm solvable within
python?  Is this a limitation of the python thread implementatio, or
will I need to dive down deeper to the underlying pthreads?  Will I
have the same problem if I rework the server to use asyncore instead of
SocketServer?