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In this paper, we analyze the performance of space-time codes by deriving a new approximation of the frame error probabilities for space-time trellis-coded modulations over quasi-static Rayleigh-fading channels. We take advantage of two techniques, the modified bounding technique and the limiting-before-averaging technique, to tighten the upper bound. In addition, we establish a theorem that enables us to reduce the computation and memory needed to calculate the frame error rate (FER) approximation. The newly derived approximation is very tight, requires only the distance spectrum of the space-time code, and can be computed through single numerical integration. Numerical results exhibit that the new approximation is much closer to the simulation results than other existing bounds are, especially in the case of one receive antenna.