This week's giveaway is in the EJB and other Java EE Technologies forum. We're giving away four copies of EJB 3 in Action and have Debu Panda, Reza Rahman, Ryan Cuprak, and Michael Remijan on-line! See this thread for details.
If this was my problem I would experiment by adding a second <Connector element right after the one for port="80" in server.xml. Since it would not handle many requests you could give it fewer threads etc.