The starting point of this paper is an argument to the conclusion that the definition of metaphysical possibility in terms of correct conceivability, conceivability informed by knowledge of relevant essences, found in Rosen (2006) is equivalent to a version of the essentialist definition of metaphysical necessity. This argument appears to show that correct conceivability is a notion of conceivability by name only and is therefore of no interest to epistemologists of modality. In this paper, I present the equivalence argument, explain (...) the idealizing assumptions involved in it and sketch a version of the conceivability approach which weakens these assumptions in order to show that the notion of correct conceivability can still play a specific limited role in the epistemology of modality. (shrink)