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Combining of space-time coded modulation (STCM) and phase sweeping transmit diversity (PSTD) is considered. The potential performance gain of space-time codes for fast fading channels can be utilized also in quasistatic fading channels by introducing quickened fading that can be obtained by employing PSTD. In addition to using separate PSTD antennas for each STCM signal, another approach where the additional PSTD antennas are shared between the STCM signals is proposed. Both approaches are shown to improve significantly the error rate performance of two considered space-time codes, which were proposed for fast fading channels, in slow Rayleigh fading.