The thesis of physical supervenience (PS) is widely understood and endorsed as the weakest assertion that all facts are tethered to the physical facts. As an exercise in exploring the constitutive commitments of an ontic view of mechanistic explanation, I entertain a weaker tethering relation, stochastic physical supervenience (SPS), the possibility of which is suggested by analogy with the apparent failure of causal determinism (CD) in certain areas of physical science. Considering this possibility helps to clarify the constitutive commitments of mechanistic explanation and to explore the motivations for accepting the PS thesis.