  We describe a new class of supersymmetric string compactifications to 4d
Minkowski space. These solutions involve type II strings propagating on
(orientifolds of) non Calabi-Yau spaces in the presence of background NS and RR
fluxes. The simplest examples have descriptions as cosets, generalizing the
three-dimensional nilmanifold. They can also be thought of as twisted tori. We
derive a formula for the (super)potential governing the light fields, which is
generated by the fluxes and certain ``twists'' in the geometry. Detailed
consideration of an example also gives strong evidence that in some cases,
these exotic geometries are related by smooth transitions to standard
Calabi-Yau or G2 compactifications of M-theory.
