The Reichenbach-Grunbaum thesis of the conventionality of simultaneity is clarified and defended by developing the consequences of the Special Theory when assumptions are not made concerning the one-way speed of light. It is first shown that the conventionality of simultaneity leads immediately to the conventionality of all relative speeds. From this result, the general-length-contraction and time-dilation relations are then derived. Next, the place of time-dilation and length-contraction effects within the Special Theory is examined in the light of the conventionality thesis. (...) The slow-transport method of synchrony is then examined in the light of these results and is shown not to provide an adequate method of uniquely determining the one-way speed of light. Finally, the general ε -Lorentz transformations for events along the x-axis are derived from three principles: the round-trip light principle, the principle of equal passage times, and the linearity principle. These principles are shown to be independent of one-way velocity assumptions, and thus may form the basis of a Special Theory of Relativity without simultaneity assumptions. (shrink)