  We consider type IIB flux compactifications on six-dimensional
SU(2)-structure manifolds with O5- and O7-planes. These six-dimensional spaces
allow not only for F_3 and H_3 fluxes but also for F_1 and F_5 fluxes. We
derive the four-dimensional N=1 scalar potential for such compactifications and
present one explicit example of a fully stabilized AdS vacuum with large volume
and small string coupling. We then discuss cosmological aspects of these
compactifications and derive several no-go theorems that forbid dS vacua and
slow-roll inflation under certain conditions. We also study concrete examples
of cosets and twisted tori and find that our no-go theorems forbid dS vacua and
slow-roll inflation in all but one of them. For the latter we find a dS
critical point with \epsilon numerically zero. However, the point has two
tachyons and eta-parameter \eta \approx -3.1.
