Logout X Session When Application Closes

I'm setting up X with TWM so that folks here can access one specific graphical application. I have it setup so one can VNC in, log-in using XDM and have said application automatically start up. What I'd like to do is have it automatically log-out of the session once that application closes. Is there a trick I can do in the xinit script, or find some way to make TWM dependent on this particular application?