  We analyze the tree-level potential of type IIB flux compactifications in
warped Calabi-Yau orientifolds, in regions of weak coupling and moderately
large complex structure. In this regime, one may approximate the flux-induced
superpotential $W$ by a polynomial on the axio-dilaton and complex structure
fields, and a significant fraction of vacua corresponds to a quadratic $W$. In
this quadratic case, we argue that vacua fall into three classes, for which one
can push the analytic description of their features. In particular, we provide
analytic expressions for the vacuum expectation values and flux-induced masses
of the axio-dilaton and complex structure fields in a large subclass of vacua,
independently of the Calabi-Yau and the number of moduli. We show that
supersymmetric vacua always contain flat directions, at least at this level of
approximation. Our findings allow to generate vast ensembles of flux vacua in
specific Calabi-Yau geometries, as we illustrate in a particular example.
