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 n
aked singularities. The recently discussed self-tuning mechanism to cancel
the cosmological constant on a brane is naturally incorporated. We show tha
t even if the vacuum energy on the brane changes, e.g. due to a phase trans
ition, the brane geometry remains insensitive to the local vacuum energy. W
e also consider the static self-tuning branes introduced earlier, and find
a solution in which the brane geometry starts to contract when the vacuum e
nergy on the brane changes.