Generalised Template Theory holds that templatic restrictions on reduplicative morphemes follow from independent, general principles. Under lexically indexed constraint theory, however, reduplicants are in no way special – morpheme-specific constraints may apply just to reduplicants. This article presents reduplication patterns in Tonkawa, which are argued to require reduplicant-specific constraints. In Tonkawa, the reduplicant is limited in size to CV, and is usually syllabified as a light syllable. Even though the language typically prefers heavy syllables word-initially, they are light if the syllable is a reduplicative prefix. This size restriction is backcopied onto the first syllable of the base. In the context of the prosodic phonology of Tonkawa, this pattern can only be understood if there is a reduplicant-specific prohibition against heavy syllables. This prohibition is formulated in terms of lexically indexed constraints on the reduplicant, which allows for a nuanced understanding of the emergent CV template.