We investigate the effective theory of type IIA string theory on six-dimensional orientifold backgrounds with SU(2)-structure. We focus on the case of orientifolds with O6-planes, for which we compute the bosonic effective action in the supergravity approximation. For a generic SU(2)-structure background, we find that the low-energy effective theory is a gauged N = 2 supergravity where moduli in both vector and hypermultiplets are charged. Since all these supergravities descend from a corresponding N = 4 background, their scalar target space is always a quotient of a SU(1, 1)/U(1) x SO(6, n)/SO(6) x SO(n) coset, and is therefore also very constrained.