One class of solutions to the strong CP problem relies on generalized parity symmetries. A minimal model of this type, constructed by Babu and Mohapatra and based on a softly broken parity symmetry, has the remarkable property that effective QCD vacuum angle $bartheta$ vanishes up to one-loop order. We compute the leading two-loop contributions to $bartheta$ in this model and estimate subleading contributions. In contrast to previous estimates, we argue that $bar theta$ is not suppressed by the weak scale, and we find contributions of order $10^{-3}$-$10^{-2}$ multiplying unknown mixing angles and phases. Thus the model does not generically address the strong CP problem, but it might be made consistent with $bartheta<10^{-10}$ in some corners of parameter space. For such non-generic parameters, $bartheta$ is still likely to be just below present bounds, and therefore provides the dominant source of hadronic EDMs. We discuss the resulting EDM phenomenology.
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