In this paper, I elucidate the main points involved in the question of the non-triviality of the conventionality of simultaneity within the kinematics of special relativity. I argue that there is an important distinction to be made between the inherited component and the sui generis component of the conventionality of simultaneity. The factual core of the kinematics of special relativity is explored, and it is shown that the Round-Trip Clock Retardation effect obtains if, and only if Winnie's Passage Time Principle holds. Some consequences of this fundamental fact are then explored. In particular, Grünbaum's view that the epistemological conventionality of simultaneity is logically prior to the physical inter-frame relativity of simultaneity is found to be based largely on what I call the inherited component of the former. Finally, a question is raised as to the very self-consistency of the claim, made by Ellis and Bowman, that standard signal synchrony and slow-transport synchrony are logically independent. In some concluding remarks, the author's general agreement with Grünbaum's conception of bridled conventionalism is indicated.