This paper demonstrates on the basis of novel data from Hungarian that contrary to received opinion, sluicing is possible inside relative clauses. It shows that sluicing can affect a relative clause to the exclusion of its relative pronoun in headless or headed relatives that can be considered non-canonical free choice expressions. In sluicing, the relative pronoun that gets stranded in the ellipsis process furthermore bears the major stress associated with the relative clause, a cross-linguistically rare possibility in languages. The findings throw a new light on theories concerned with the syntactic licensing of sluicing and ellipsis in general, pointing at the crucial role of prosody.