  Recently the global variation of the Planck mass in the General Relativistic
Einstein-Hilbert action was proposed as a self-tuning mechanism of the
cosmological constant preventing vacuum energy from freely gravitating. We show
that this global mechanism emerges for generic local scalar-tensor theories
with additional coupling of the scalar field to the field strength of a
three-form gauge field that turns the scalar field constant on the domain of
the action. Evaluation of the resulting integral constraint equation over the
observable Universe yields a self-consistent framework with General
Relativistic field equations and arbitrary radiatively stable residual
cosmological constant. We argue that the expectation value for this residual is
in good agreement with the magnitude of the observed cosmic acceleration.
