  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 $W_0 \approx 2 \times 10^{-8}$ 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.
