  We show that every negative definite configuration of symplectic surfaces in
a symplectic 4--manifold has a strongly symplectically convex neighborhood. We
use this to show that, if a negative definite configuration satisfies an
additional negativity condition at each surface in the configuration, and if
the complex singularity with resolution diffeomorphic to a neighborhood of the
configuration has a smoothing, then the configuration can be symplectically
replaced by the smoothing of the singularity. This generalizes the symplectic
rational blowdown procedure used in recent constructions of small exotic
4--manifolds.
