A current issue in the study of planetary nebulae with close binary central stars (CSs) is the extent to which the binaries affect the shaping of the nebulae. Recent studies have begun to show a high coincidence rate between nebulae with large-scale axial or point symmetries and close binary stars. In addition, combined binary-star and spatiokinematic modeling of the nebulae have demonstrated that all of the systems studied to date appear to have their central binary axis aligned with the primary axis of the nebula. Here we add two more systems to the list, the CSs and nebulae of NGC 6337 and Sp 1. We show both systems to be low inclination, with their binary axis nearly aligned with our line of sight. Their inclinations match published values for the inclinations of their surrounding nebulae. Including these two systems with the existing sample statistically demonstrates a direct link between the central binary and the nebular morphology. In addition to the systems’ inclinations we give ranges for other orbital parameters from binary modeling, including updated orbital periods for the binary CSs of NGC 6337 and Sp 1.