  Self tuning is one of the few methods for dynamically cancelling a large
cosmological constant and yet giving an accelerating universe. Its drawback is
that it tends to screen all sources of energy density, including matter. We
develop a model that tempers the self tuning so the dynamical scalar field
still cancels an arbitrary cosmological constant, including the vacuum energy
through any high energy phase transitions, without affecting the matter fields.
The scalar-tensor gravitational action is simple, related to cubic Horndeski
gravity, with a nonlinear derivative interaction plus a tadpole term. Applying
shift symmetry and using the property of degeneracy of the field equations we
find families of functions that admit de Sitter solutions with expansion rates
that are independent of the magnitude of the cosmological constant and preserve
radiation and matter dominated phases. That is, the method can deliver a
standard cosmic history including current acceleration, despite the presence of
a Planck scale cosmological constant.
