Generalized processor sharing (GPS) is an idealized fluid discipline with a number of desirable properties. Its packetized version PGPS is considered to be a good choice is a packet scheduling discipline to guarantee quality-of-service in IP and ATM networks. The existing connection admission control (CAC) frameworks for GPS result in a conservative resource allocation. We propose an optimal CAC algorithm for a GPS scheduler, for leaky-bucket constrained connections with deterministic delay guarantees. Our numerical results show that the optimal CAC results in a higher network utilization than the existing CACs.