In this paper, I propose an optimality-theoretic account of the generalisation that deletion processes that apply to intervocalic biconsonantal clusters canonically delete the first consonant (schematically, VC1C2V → VC2V). The approach to contextual neutralisation proposed here has two main components. First, I follow the licensing-by-cue framework (e.g. Steriade 1997) in identifying ‘weak’ elements as those without strong perceptual cues. Second, I argue that the constraints responsible for contextual neutralisation ‘target’ weak elements. This approach captures the deletion generalisation above, because the relevant targeted constraint prefers only the correct output VC2V (from which the weak consonant C1 has been removed), not the incorrect output VC1V. Intuitively, the representation containing a weak element (VC1C2V) is compelled to neutralise to a representation that is perceptually very similar (VC2V). The targeted-constraint approach is formalised by replacing the standard violation-based definition of OT optimisation with a new definition – which is equivalent except when ‘targeted’ constraints are involved – based on harmonic orderings. The approach is shown to extend to certain cases of (i) contextually determined feature neutralisation and (ii) phonological opacity.