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The increasing variety and complexity of traffic in today's mobile wireless networks means that there are more restrictions placed on a network in order to guarantee the individual requirements of the different traffic types and users. Call admission control (CAC) plays a vital role in achieving this. We propose a precision predictive CAC (PPCAC) scheme in which existing methods to determine the call occupancy distribution in each cell are modified in order to predict the number of calls of each individual service. Information about the channel usage of each service is then used to calculate the capacity of the cell to ensure that each service's bit error rate (BER) requirements are met. Priorities assigned to each service are used to allocate the network capacity. An expression for the handoff dropping probability is derived and the acceptance rate for each service is calculated in order to meet the guaranteed quality of service (QoS). Each call is then accepted with equal probability throughout the duration of a control period. The new call acceptance rate is adjusted to ensure that the dropping probability remains fixed. The complexity of this algorithm is offset by the fact that most of the computations can be completed offline and it only requires readily available network measurements. Simulations conducted in a CDMA environment with voice, short message service (SMS) and World Wide Web (WWW) sources show that the proposed CAC can successfully meet the hard restraint on the dropping probability and guarantee the required BER for multiple services.