Theories which spontaneously break spacetime parity can solve the strong CP problem. They usually have few free parameters and are therefore very predictive, but their landscape remains quite unexplored. I will present a construction based on a complete mirror copy of the standard model, linked to our world by colored portal fields. Those induce the partial spontaneous breaking of the color groups, which yields a vanishing theta angle at low energies. The lightest BSM fields could be colored (pseudo-Goldstone or vector) bosons, while the lightest of the heavy vectorlike fermions typical of parity models can play the role of dark matter.