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We design a new rate-5/4 full-diversity orthogonal space-time block code (STBC) for QPSK and 2 transmit antennas (TX) by enlarging the signalling set from the set of quaternions used in the Alamouti code. Selective power scaling of information symbols is used to guarantee full-diversity while maximizing the coding gain (CG) and minimizing the transmitted signal peak-to-minimum power ratio (PMPR). The optimum power scaling factor is derived analytically and shown to outperform schemes based only on constellation rotation while still enjoying a low-complexity maximum likelihood (ML) decoding algorithm. Finally, we extend our designs to the case of 4 TX by enlarging the set of quasi-orthogonal STBC with power scaling. Extensions to general M-PSK constellations are straightforward.