Trellis-coded modulation (TCM) has become a powerful tool to encode digital signals over band limited channels. Multidimensional TCM offers higher bandwidth utilization than two dimensional modulation (2D). Unfortunately, the advantage of coding is only achieved when the Maximum-Likelihood-Sequence-Estimation (MLSE) algorithm is used at the decoder. A practical implementation of MLSE is the Viterbi Algorithm (VA) decoder. It requires less stored number of sequences together with their computed Euclidean distances (cost) from the received sequence than MLSE. The presence of signal distortion introduced by practical channels, adds additional arithmetic operations and storage requirements to VA. This work presents new detection schemes for distorted four dimensional (4D) Ungerboeck's TCM signals. These include both fixed and variable (adaptive) complexity detection processes. A modification to the nonlinear equalizer and reduced state detectors, known before, are also presented. A novel technique to force the detection towards its minimum complexity is studied. The proposed technique mainly relies on the noise level estimation. This estimation together with the theoretical analysis of the proposed detection process are verified using computer simulation programs. The results of computer simulation tests show that the proposed algorithm gives an encouraging performance with very low complexity at high signal to noise power ratios.