The paper shows that some continuous phase modulation (CPM) schemes have some properties that allow a near optimum reception with very low complexity. The proposed reception method applies simultaneously three techniques for complexity reduction of CPM receivers, which have been previously object of separate analysis with additive white Gaussian noise (AWGN). These techniques are: first-quadrant metrics calculus on a F-dimensional Walsh space, derivation of the other quadrant metrics using a no loss derivation algorithm and finally the use of constrained complexity maximum likelihood sequence detection (MLSD) using the M-algorithm. The cumulative effect on total performance loss is negligible and no more than the sum of the partial losses due to the Walsh space and the M-algorithm, known to be negligible when observing the respective standalone rules for the complexity reduction limits.