The formal and operational significance of the choice of clock synchronization in relativity is reviewed, along with the historical debate over the associated choice of the one-way speed of light. Kinematic test theories generalising special relativity are recast in a nonstandard synchronisation. In particular, the Mansouri-Sexl test-theory is generalised to avoid a conflict between its interpretation and its gauge choice. Corresponding adjustments to the interpretation of recent experimental tests of relativity are presented. A test-theory for local Lorentz invariance is derived for a noninertial observer in a space of arbitrary curvature using differential geometric techniques and the Frenet frame. The Sagnac effect in a ring laser is considered for bounding the parameters of this theory.