  We prove that the supercritical one-dimensional contact process survives in
certain wedge-like space-time regions, and that when it survives it couples
with the unrestricted contact process started from its upper invariant measure.
As an application we show that a type of weak coexistence is possible in the
nearest-neighbor ``grass-bushes-trees'' successional model introduced in
Durrett and Swindle (1991).
