Help reconfiguring RT with lighttpd and fastcgi

I am using RT with lighttpd and FastCGI. Right now, RT is running on
an internal web server and it is the only web app running on it.
What I’d like to do is configure lighttpd so that instead of going to
http://my.web.server to get to RT, I can instead use http://
my.web.server/rt and have another app run at http://my.web.server/
inventory. Could someone tell me what I need to do to accomplish
this? Thanks!!