Vacua with Small Flux Superpotential.

We describe a method for finding flux vacua of type IIB string theory in which the Gukov-Vafa-Witten superpotential is exponentially small. We present an example with W_{0}≈2×10^{-8} on an orientifold of a Calabi-Yau hypersurface with (h^{1,1},h^{2,1})=(2,272), at large complex structure and weak string coupling.