Summary: This paper describes a decomposition algorithm to estimate the performance of a call center with two types of customers and two server categories. In this system specialized servers can process only one customer type, while flexible servers handle both types. The algorithm divides the systemrsquos state space into regions, and simple approximate models find the conditional system performance within each region. While the procedure described here is tailored for a system with a priority queue discipline and two customer classes, it can be adapted for systems with FCFS queue disciplines and for systems with more than two customer types. Performance measures generated by the procedure are sufficiently accurate for many service system design decisions, such as setting telephone call center staffing levels and long-term capacity planning. The procedure is also extremely fast, and its computational requirements do not grow with system congestion. Numerical tests demonstrate that its running time is significantly lower than traditional numerical methods for generating approximations. As an example of its use, we employ the procedure to demonstrate the benefits of server flexibility in a particular telephone call center.