This paper does two things. Firstly, it clarifies the way that phenomenological data is meant to constrain cognitive science according to enactivist thinkers. Secondly, it points to inconsistencies in the "Radical Enactivist' handling of this issue, so as to explicate the commitments that enactivists need to make in order to tackle the explanatory gap. I begin by sketching the basic features of enactivism in sections 1–2, focusing upon enactive accounts of perception. I suggest that enactivist ideas here rely heavily upon the endorsement of a particular explanatory constraint that I call the structural resemblance constraint (SRC), according to which the structure of our phenomenology ought to be mirrored in our cognitive science. Sections 3–5 delineate the nature of, and commitment to, SRC amongst enactivists, showing SRC's warrant and implications. The paper then turns to Hutto and Myin's (2013) handling of SRC in sections 6–7, highlighting irregularities within their programme for Radical Enactivism on this issue. Despite seeming to favour SRC, I argue that Radical Enactivism's purported compatibility with the narrow (brain-bound) supervenience of perceptual experience is in fact inconsistent with SRC, given Hutto and Myin's phenomenological commitments. I argue that enactivists more broadly ought to resist such a concessionary position if they wish to tackle the explanatory gap, for it is primarily the abidance to SRC that ensures progress is made here. Section 8 then concludes the paper with a series of open questions to enactivists, inviting further justification of the manner in which they apply SRC.