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Call admission control (CAC) is one of the important means to guarantee quality of service (QoS) in telecommunication systems. This is true in mobile networks due to their limited capacity. In second-generation (2G) GSM systems, the cell has static coverage and capacity, therefore, the call is rejected if all channels in the given cell are occupied. In third generation (3G) systems, such as UMTS, cells have dynamic coverage and capacity that depend on the interference levels and the number of active connections in the cell. In this study, a new sophisticated multi-cell CAC algorithm is presented that uses the soft handover feature of the UMTS systems to provide multiple goals: first, to provide efficient utilization of the available capacity; secondly, to protect the QoS of existing connections; and lastly, to prevent the loss of coverage resulting from the so-called "cell breathing". The algorithm works on balancing the load over the network by transferring some connections from the overloaded cells to the neighboring cells with lighter load. Therefore, it achieves more balanced utilization over the whole network. The algorithm is evaluated on a network cluster of seven cells via detailed simulation under different traffic and interference conditions.