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We propose and analyze in this paper two new adaptive power controlled minimum selection generalized selection combining (MS-GSC) diversity schemes. The key idea behind these two schemes is to request the transmitter to vary its power level during very adverse channel conditions in order to communicate with the minimum required quality of service. For each scheme, four power control variants accounting for practical implementation constraints including discrete power levels and transmitter gain saturation are proposed and studied. Selected numerical examples, show that ideal continuous power control lowers the average bit error rate of MS-GSC and makes it always meet the specified target quality of service at the expense of an increase in the transmitter gain. Additional numerical examples, show that the power control variants that take into account practical implementation constraints conserve the main features of the ideal continuous power algorithm.