  Well tempering is one of the few classical field theory methods for solving
the original cosmological constant problem, dynamically canceling a large
(possibly Planck scale) vacuum energy and leaving the matter component intact,
while providing a viable cosmology with late time cosmic acceleration and an
end de Sitter state. We present the general constraints that variations of
Horndeski gravity models with different combinations of terms must satisfy to
admit an exact de Sitter spacetime that does not respond to an arbitrarily
large cosmological constant. We explicitly derive several specific
scalar-tensor models that well temper and can deliver a standard cosmic history
including current cosmic acceleration. Stability criteria, attractor behavior
of the de Sitter state, and the response of the models to pressureless matter
are considered. The well tempered conditions can be used to focus on particular
models of modified gravity that have special interest -- not only removing the
original cosmological constant problem but providing relations between the free
Horndeski functions and reducing them to a couple of parameters, suitable for
testing gravity and cosmological data analysis.
