My question is: does phenomenal consciousness have a critical role in explaining the way conscious perceptions achieve objective import? I approach it through developing a dilemma I label 'Burge's Challenge', which is implicit in his approach to perceptual objectivity. It says, crudely: either endorse the general structure of his account of how objective perceptual import is achieved (an account I label 'Caused Representation'), and give up on a role for consciousness. Or, relinquish Caused Representation, and possibly defend a role for consciousness. Someone I call Burge* holds we should embrace the first horn of the dilemma. A second response, roughly the relationalist approach, opts for the second horn. The third option, implicit in many current approaches to perceptual consciousness, is to reject the dilemma. The paper argues for a version of the second response. The key argument turns on the development of a sceptical challenge to justify the assumption that we perceive particular intrinsic property instantiations, rather than their structural equivalents. The suggestion will be that only the relationalist approach can meet it in the way we think it is met. If this is right, there is a prima facie case for taking relationalist responses to the dilemma seriously. I end with two objections to this response, which might be made by the real Burge in defence of opting for the first horn of the dilemma, and by phenomenal intentionalists in defence of rejecting the dilemma. I use discussion of these to highlight one of the main issues that should be pursued in order to make good the claim that we should embrace the horn of the dilemma that Burge* rejects.