The impact of the M-algorithm on continuous phase modulation (CPM) detection is analyzed when replacing the common Viterbi algorithm (VA) on the maximum likelihood sequence detection (MLSD) block. The algorithm is presented as a reduced complexity sequence detection algorithm in which not all transitions are propagated, being only retained a small subset of paths. A rule is found concerning the lower limit of the mandatory number of paths to retain, using simulations with additive white gaussian noise (AWGN) when detecting simple catastrophic schemes and two optimum gain schemes, in the sense they are two of the rare coincident with their respective minimum Euclidean upper bounds. The M-algorithm proves near optimum performance for very low ratios of number of traced states per total number of states.