This paper argues against the view of intrusive [r] as a synchronically arbitrary insertion process. Instead, it is seen as a phonologically natural process, which can be modelled within the framework of Optimality Theory (OT). Insertion of [r] in phonologically restricted environments is a consequence of a more general theory of consonant epenthesis outlined here. This theory ties epenthesis in with the notion of prominence and strives to formalize a general theory of epenthesis which explains why glottal stops and glides are crosslinguistically frequently found epenthetic consonants, although in different prosodic contexts. I argue that glottal stops are optimal margin consonants and thus inserted in margin positions (e.g. word-initially) while glides are optimal peak consonants, inserted in peak positions (e.g. as hiatus breakers). This hypothesis is derived from sonority-based prominence scales [Prince, A., Smolensky, P., 1993. "Optimality Theory: Constraint Interaction in Generative Grammar." Ms. Rutgers University and the University of Colorado at Boulder]. Intrusive [r] can then be understood as the optimal consonant in a peak position when glide formation is blocked, because [r] is the most sonorous possible element in this position. Spreading-based or perceptually grounded accounts of intrusive [r] are consequently rejected under this approach. (Contains 2 figures.)