Two important Quality-of-Service (QoS) measures for current cellular networks are the fractions of new and handoff “calls” that are blocked due to unavailability of “channels” (radio and/or computing resources). Based on these QoS measures, we derive optimal admission control policies for three problems: minimizing a linear objective function of the new and handoff call blocking probabilities (MINOBJ), minimizing the new call blocking probability with a hard constraint on the handoff call blocking probability (MINBLOCK) and minimizing the number of channels with hard constraints on both of the blocking probabilities (MINC). We show that the well-known Guard Channel policy is optimal for the MINOBJ problem, while a new Fractional Guard Channel policy is optimal for the MINBLOCK and MINC problems. The Guard Channel policy reserves a set of channels for handoff calls while the Fractional Guard Channel policy effectively reserves a non-integral number of guard channels for handoff calls by rejecting new calls with some probability that depends on the current channel occupancy. It is also shown that the Fractional policy results in significant savings (20-50\%) in the new call blocking probability for the MINBLOCK problem and provides some, though small, gains over the Guard Channel policy for the MINC problem. Further, we also develop computationally inexpensive algorithms for the determination of the parameters for the optimal policies.