Modern Japanese has a set of morphophonemic alternations known collectively as rendaku that involve initial consonants in second elements of compounds, as in /jama+dera/ ‘mountain temple’ (cf. /tera/ ‘temple’). An alternating element like /tera/ ~ /dera/ has an initial voiced obstruent in its rendaku allomorph and an initial voiceless obstruent in its non-rendaku allomorph. Lyman's Law blocks rendaku in a second element containing a medial voiced obstruent. This paper gives three arguments that Lyman's Law originated as a constraint prohibiting prenasalisation in consecutive syllables. First, constraints on similar consonants in close proximity generally apply not to voicing but to features with phonetic cues that are more spread out, such as prenasalisation. Second, in some Japanese dialects with prenasalised voiced obstruents, rendaku cannot occur if it would result in adjacent syllables containing these marked consonants. Third, phonographically attested Old Japanese compounds are consistent with a constraint on adjacent syllables.