  We introduce a new brane-world model in which the bulk solution consists of
outgoing plane waves. This is an exact solution to string theory with no naked
singularities. The recently discussed self-tuning mechanism to cancel the
cosmological constant on a brane is naturally incorporated. We show that even
if the vacuum energy on the brane changes, e.g. due to a phase transition, the
brane geometry remains insensitive to the local vacuum energy. We also consider
the static self-tuning branes introduced earlier, and find a solution in which
the brane geometry starts to contract when the vacuum energy on the brane
changes.
