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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 paper, we introduce two simple joint adaptive modulation and power allocation (AMP) methods for vr-STBCs so as to maximize the total throughput under constraints of transmit power limit and bit error rate (BER) requirements: tightest SER constraint method and iterative method. The tightest symbol error rate (SER) constraint method, which uses tightest SER constraints to guarantee the BER constraints for every modulation orders, is simple but gives a low bound for optimum capacity, and the iterative method gives local optimum capacity with somewhat higher complexity than the former one. Numerical results show that both proposed schemes can enhance the performance of existing vr-STBCs by achieving greater throughput as well as satisfying BER requirements. Moreover, we can see that the capacity loss caused by the tightest SER constraint is not serious comparing to the iterative one, and the iterative method doesn't increase the calculational complexity seriously. We can see that the proposed AMP schemes show more throughput gain as diversity order is decreasing, comparing to the conventional ones, since the proposed adaptive schemes can bring more gain as the channel fluctuation becomes greater.