Solving the Strong $\mathrm{CP}$ Problem without the Peccei-Quinn Symmetry

A simple theorem is proved about the $\bar{\theta }$ parameter in grand unified models with spontaneous $\mathrm{CP}$ symmetry breaking. This theorem states two conditions on such models which, if fulfilled, imply that $\bar{\theta }$ is zero at tree level. Models which fulfill these conditions are generalizations of a recent model of Nelson and are easy to construct.