Using Takahashi & Fox (2005) as an exemplar, this paper argues that analyses of English ellipsis that make recourse to a MaxElide constraint (or a theoretical reduction thereof) are misguided, and that one must look past MaxElide to explain the distribution of acceptability in the elliptical rebinding constructions that MaxElide was originally invoked to explain. A novel analysis is outlined which attributes the unacceptability observed in the rebinding dataset to an inability to satisfy a more restrictive, reflexive version of Takahashi & Fox's (ibid.) Parallelism condition on ellipsis recoverability.