In this paper, we evaluate a Call Admission Control (CAC) scheme suitable for W-CDMA networks accommodating multiple service-classes. In such networks, the distinction between new and handoff traffic is very important. A simple CAC scheme can distinguish calls between the two traffic types by setting different thresholds for call admission. This simple CAC scheme is evaluated in respect of blocking probabilities of both new and handoff calls. To this end, we formulate aggregated Markov chains, which describe both new-call and handoff-call arrival processes, under the assumption that they are Poisson or quasi-random. Based on these Markov chains we derive recurrent and computationally efficient formulas for the calculation of the system state probabilities. Consequently, we calculate new-call and handoff-call blocking probabilities. The analytical results are verified through simulation and found to be quite satisfactory.