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We compare low-complexity schemes for soft-output detection of continuous phase modulations (CPMs). In particular, we address the problem of minimizing the complexity of the front end filters and that of the trellis exploited by the detection algorithm, with the aim of assuring a negligible performance degradation with respect to the optimal full-complexity receiver. We show that the approach providing the simplest front end is that based on the CPM decomposition proposed by Moqvist and Aulin. On the other hand, we prove that the most convenient solution in terms of trellis complexity is provided by the CPM decomposition proposed by Mengali and Morelli, possibly combined with suitable techniques for reduced trellis search.