  Tentative observations and theoretical considerations have recently led to
renewed interest in models of fundamental physics in which certain
``constants'' vary in time. Assuming fixed black hole mass and the standard
form of the Bekenstein-Hawking entropy, Davies, Davis and Lineweaver have
argued that the laws of black hole thermodynamics disfavor models in which the
fundamental electric charge $e$ changes. I show that with these assumptions,
similar considerations severely constrain ``varying speed of light'' models,
unless we are prepared to abandon cherished assumptions about quantum gravity.
Relaxation of these assumptions permits sensible theories of quantum gravity
with ``varying constants,'' but also eliminates the thermodynamic constraints,
though the black hole mass spectrum may still provide some restrictions on the
range of allowable models.
