We prove that an irreducible 3-manifold with fundamental group that satisfies a certain grouptheoreticproperty 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 groups. Moreover, we show that a taut-sutured compression body has a finite-sheeted cover with a depth one taut-oriented foliation.