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Call admission control (CAC) is important for cellular wireless networks to provide quality-of-service (QoS) requirements to users. Static and adaptive CAC schemes, respectively, make unrealistic assumptions about the distributions of the handoff call arrival process and the number of users in a cell. Handoff arrivals are usually assumed to follow Poisson process in static CAC schemes for Poisson new call arrivals and exponentially distributed call holding and cell residence times. We use a simple proof to show that this assumption of Poisson handoff arrival process is not justified for a two-cell wireless network. In general, we find that the handoff process can be captured by a two-dimensional Markov chain. We propose a novel adaptive CAC scheme for the two-cell system which accepts a new call if it can guarantee, with a certain probability, that a user's call will be maintained irrespective of its (his/her) movement in the system. Then, we extend this adaptive scheme for multiple-cell network. We develop another variant of this adaptive scheme which we call fractional adaptive scheme. Both the adaptive and fractional adaptive schemes are found to outperform the guard channel scheme in controlling the handoff failure probability in a cellular wireless network.