  We explore a family of generalised scalar-tensor theories that exhibit
self-tuning to low scale anti de Sitter vacua, even in the presence of a large
cosmological constant. We are able to examine the linearised fluctuations about
these vacua and compute the corresponding amplitude. Thanks to a subtle
interplay between a weak scalar coupling and a low scalar mass, it is possible
to exhibit self-tuning and compatibility with solar system tests of gravity
without resorting to non-linearities and unreliable screening mechanisms. The
weakness of the scalar coupling and the correspondingly slow response to vacuum
energy phase transitions may present some interesting possibilities for
connecting early universe inflation to the cancellation of vacuum energy.
