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Variable-rate space-time block codes (vr-STBCs) without any feedback can support different transmission rates and unequal error protection (UEP) which are needed for multimedia communications. Assuming necessary feedback, in this letter, we introduce a joint adaptive modulation and power allocation (AMP) for vr-STBCs so as to maximize the total throughput under constraints of transmit power limit and error requirements. Based on a Lagrangian multiplier method, optimum modulation orders and power levels are provided for the transmitter. Numerical results show that the proposed AMP enhances the throughput of existing vr-STBCs up to 20% with very limited feedback, e.g., at most 3-5 bits feedback.