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Motivated by combinatorial optimization theory, we propose an algorithmic power allocation method that minimizes the total transmitting power in transmitter diversity systems, provided that the instantaneous Bit-Error-Rate (BER) is not greater than a predetermined value. This method applies to many practical applications where the power transmitted by each antenna is constrained. We also provide closed-form expressions for the average total transmitted power for the case of two transmitting antennas operating in Rayleigh fading, and the average number of active antennas at the transmitter assuming Nakagami-m fading channels. Simulations and numerical results show that, compared to the conventional equi-power scheme, the proposed model offers a considerable reduction in the total transmitting power and the average number of active antennas, without loss in error performance.