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The design criteria for space-time codes under slow flat Rayleigh fading environments are well known to be the rank criterion and the determinant criterion. However, the derivation of these two criteria is based on the assumption that the signal-to-noise ratio (SNR) is sufficiently high. Hence these criteria are loose when the SNR does not satisfy this assumption. In this letter, we consider this practical issue and derive tighter design criteria for moderate and low SNRs. Some new space-time trellis codes are found based on the new criteria through computer search. Simulation results show that these codes outperform existing codes under their designed SNR conditions.