This paper introduces a centralized admission control mechanism, referred to as Threshold-based Blocking Differentiation (TBDijf), to differentiate the blocking probability experienced by various service classes in a circuit switched WDM network. The mechanism is based on multiple class-thresholds that indicate the minimum amount of capacity that must be available, prior to accommodating a request for a given service class. The performance of TBDiff is studied by means of an analytical framework and also an event-driven simulator. The results show a thorough matching of the analytical and simulation results and also demonstrate that high blocking differentiation among service classes can be obtained, without excessively increasing the overall (average) network blocking probability.