Too many open sockets error in Tomcat 5.5

Our company recently started a new project. Our primary client is the first one to use it, and use they have. I've suspected they've been putting an unusually high load on our servers, and tonight it was confirmed when our server stopped handling requests, refusing them and then generating "Too many open files" errors in the Tomcat log files referring to my Tomcat SSL keystore. After doing some brief research on the error, I've discovered that this can happen when the Tomcat element in server.xml is configured with too few 'maxThreads' and a too low an 'acceptCount'. I've since tripled the number of threads and acceptable connections. Hopefully this will resolve things.