  We prove that an irreducible 3-manifold whose fundamental group satisfies a
certain group-theoretic property called RFRS is virtually fibered. As a
corollary, we show that 3-dimensional reflection orbifolds and arithmetic
hyperbolic orbifolds defined by a quadratic form virtually fiber. These include
the Seifert Weber dodecahedral space and the Bianchi orbifolds. Moreover, we
show that a taut sutured compression body has a finite-sheeted cover with a
depth one taut-oriented foliation.
