An optimality-theoretic (OT) approach to the phonology of the verbal phrase in Nzema, a Niger-Congo language, is presented. The analysis accounts for ATR harmony spreading from roots to prefixes, nasal homorganicity in nasal-obstruent clusters, and the opacity found in assimilation in nasal-obstruent clusters. ATR is assumed to be specified in the input on certain vowels in certain roots and then spread leftward onto verbal prefixes. A combination of constraints on association line linking and delinking and an alignment constraint to account for spreading provides a relatively straightforward account of the ATR harmony. The case of nasal homorganicity in nasal-obstruent clusters is also relatively straightforward from an OT perspective. A pair of faithfulness constraints ranked with respect to a constraint requiring place features to be shared by the components of a cluster are sufficient to account for most of the data. An additional positional faithfulness constraint on onsets is required to account for homorganicity in nasal-nasal clusters. Finally, individual faithfulness constraints and a conjoined faithfulness constraint are among those used to account for the assimilation of obstruents to nasals in voicing (in the case of voiceless obstruents) and in nasality (in the case of voiced obstruents).