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Spatial transmit diversity systems in mobile communications utilize either different antennas, polarization, or beams. Whereas separated antennas carry the same power on average, the average channel gain might vary for different polarizations or beams. Thus, the optimum tradeoff between channel gain and diversity gain has to be found. It is important to determine which allocation of the limited transmit power over the available transmit diversity branches is optimum. As optimization criterion, the outage capacity is applied for a given outage probability level. By means of numerical optimization techniques, the optimum power allocation is derived for frequency Rayleigh fading. The numerical results show that diversity branches with higher channel gain are always allocated more power, i.e. a poor channel gain is not compensated by the transmit power. Furthermore, the performance of an even power allocation over the optimum set of transmit diversity branches is very near to the optimum power allocation.