In Icelandic, and in most dialects of Faroese, the fundamental laryngeal stop contrast is one of aspiration. This contrast is neutralized in certain positions, following patterns which appear problematic for perceptually-based theories (licensing by cue). In postvocalic onset position, a cue-rich environment, the contrast is absent in Icelandic. Most dialects neutralize to unaspirated [p, t, k], whereas others have postaspirated [ph, th, kh] instead. In the latter case, the appearance of loanwords with intervocalic [p, t, k] is now creating an incipient aspiration contrast, undoing the previous neutralization pattern. The implications of these facts for Optimality Theory (Richness of the Base) are discussed. In certain dialects of Faroese, such postvocalic singleton onsets are realized as PREaspirated [hp, ht, hk]. Curiously, this preaspiration is suppressed in precisely the contexts where it ought to be most salient. An OT analysis is developed to account for this distribution.