This paper provides an Optimality Theoretic account of how Hungarian learners of English acquire /[epsilon]/ and /[ash]/. It is hypothesized that as the learners' pronunciation becomes more nativelike, L1 transfer substitutions will diminish; non-transfer substitutions will be especially prevalent in the intermediate stages, and that all learners will have equal or greater success with the similar segment /[epsilon]/ than with the unfamiliar segment /[ash]/. A study involving eight Hungarian ESL learners and four American English subjects largely supports these hypotheses. (Contains 6 figures, 2 tables, and 2 notes.)