Trellis coded modulation (TCM) schemes are used in many bandwidth-efficient systems. Typically, a TCM system employs a high-rate convolutional code, which leads to a high complexity of the Viterbi decoder (VD) for the TCM decoder, even if the constraint length of the convolutional code is moderate. High-speed, low-power design of Viterbi decoders for trellis coded modulation (TCM) systems is presented. An adaptive decoding algorithm, which is a modification of the Viterbi algorithm (VA) is presented. For a given code, the proposed algorithm yields nearly the same error performance as the VA while requiring a substantially smaller average number of computations. Unlike most of the other suboptimum algorithms, this algorithm is self-synchronizing. If the transmitted path is discarded, the adaptive Viterbi algorithm (AVA) can recover the state corresponding to the transmitted path after a few trellis depths. It is well known that the Viterbi decoder (VD) is the dominant module determining the overall power consumption of TCM decoders. We propose a pre-computation architecture incorporated with T-algorithm for VD, which can effectively reduce the power consumption without degrading the decoding speed much. A general solution to derive the optimal pre-computation steps is also given in the paper. Implementation result of a VD for a rate-3/4 convolutional code used in a TCM system shows that compared with the full trellis VD, the precipitation architecture reduces the power consumption by as much as 15% without performance loss.