The answers to many important performance related questions with multiclass queueing models depends upon having estimates for the service times of different classes of jobs. We present a general approach to infer the per-class service times at different servers in an environment where only server throughput, utilization and per-class response time measurements are available. The per-class service times are solutions to an optimization problem with queueing-theoretic formulas in the objective and constraints. We further study the impact of the variance of service times on the variance of response times. A few case studies are presented to demonstrate the power of our approach.