In this paper, we consider iterative detection over bandpass channels that introduce an unknown phase rotation in the transmitted signal. This work focuses on the comparison between two adaptive detection strategies for trellis-based coded modulation: limited-tree-search (LTS) detection, obtained by reducing a tree search to a limited trellis search, and truncated-memory (TM) detection, based on channel-memory truncation, which automatically leads to a trellis search. Both strategies are used to derive trellis-based forward-backward (FB) algorithms. A quantitative analysis based on simulations, with various coding and modulation schemes, is carried out to evaluate and compare the two approaches. The results show that the channel-phase dynamics should significantly influence the choice of the detection strategy: For low-phase variations, LTS algorithms are a simple and reasonable choice, while for moderate to fast phase variations, TM algorithms show a considerable robustness.