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The joint power control and base station assignment for the downlink is considered in this paper. Based on the results and observations of previous work we present an algorithm that finds a feasible joint base assignment and transmission power vector in the downlink. We show that under some conditions the algorithm also minimizes the sum of downlink powers. Interestingly, there is not always a Pareto optimal power vector for the joint problem in the downlink as is the case in the uplink. This fact is demonstrated through a counterexample.