This paper discusses the design of good space-time trellis codes in terms of distance spectrum. We run two exhaustive searches in the design of good space-time trellis codes. We found that although a lot of space-time trellis codes exist by maximizing the minimum effective Hamming distance and the minimum effective product distance, when the distance spectrum is taken into account, the number of good space-time trellis codes is quite limited. We present some good space-time trellis codes with better distance spectrum. Simulation results demonstrate that these new codes have better performance than previous codes.