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We study the simplest theories with exact spacetime parity that solve thestrong CP problem and successfully generate the cosmological baryon asymmetryvia decays of right-handed neutrinos. Lower bounds are derived for the massesof the right-handed neutrinos and for the scale of spontaneous parity breaking,$v_R$. For generic thermal leptogenesis, $v_R \gtrsim 10^{12}$ GeV, unless thesmall observed neutrino masses arise from fine-tuning. We compute $v_R$ interms of the top quark mass, the QCD coupling, and the Higgs boson mass andfind this bound is consistent with current data at $1 \sigma$. Future precisionmeasurements of these parameters may provide support for the theory or, if$v_R$ is determined to be below $10^{12}$ GeV, force modifications. However,modified cosmologies do not easily allow reductions in $v_R$ -- no reduction ispossible if leptogenesis occurs in the collisions of domain walls formed atparity breaking, and at most a factor 10 reduction is possible with non-thermalleptogenesis. Standard Model parameters that yield low values for $v_R$ canonly be accommodated by having a high degree of degeneracy among theright-handed neutrinos involved in leptogenesis. If future precisionmeasurements determine $v_R$ to be above $10^{12}$ GeV, it is likely thathigher-dimensional operators of the theory will yield a neutron electric dipolemoment accessible to ongoing experiments. This is especially true in a simpleUV completion of the neutrino sector, involving gauge singlet fermions, wherethe bound from successful leptogenesis is strengthened to $v_R \gtrsim 10^{13}$GeV.

Leptogenesis in Parity Solutions to the Strong CP Problem and Standard Model Parameters