  We introduce an ansatz which allows us to solve the supersymmetry equations
for warped N=1 AdS4 type II supergravity compactifications of general
SU(3)xSU(3) structure. As a byproduct we obtain a set of necessary conditions
which every supersymmetric AdS4 vacuum should obey. The case of AdS4
compactifications of IIB on manifolds of static SU(2) structure is examined in
detail. Several examples of solutions are presented. In the limit of
four-dimensional Minkowski space, we present examples of supersymmetric IIB
warped compactifications with partially localized NS5- and D5-branes. We also
present `massive' non-supersymmetric AdS4xM6 solutions of IIA, where M6 can be
any six-dimensional Einstein-Kaehler manifold.
