We consider reduced crossed products of twisted C*-dynamical systems over C*-simple groups. We prove there is a bijective correspondence between maximal ideals of the reduced crossed product and maximal invariant ideals of the underlying C*-algebra, and a bijective correspondence between tracial states on the reduced crossed product and invariant tracial states on the underlying C*-algebra. In particular, the reduced crossed product is simple if and only if the underlying C*-algebra has no proper non-trivial invariant ideals, and has a unique tracial state if and only if the underlying C*-algebra has a unique invariant tracial state. We further show that the reduced crossed product satisfies an averaging property analogous to Powers’ averaging property. The dynamical systems are not required to be exact, and our results are new even in the non-twisted case.