ABSTRACT As part of a survey to find close binary systems among central stars of planetary nebula, we present two newly discovered binary systems. GALEX J015054.4+310745 is identified as the central star of the possible planetary nebula Fr 2-22. We find it to be a single-lined spectroscopic binary with an orbital period of 0.2554435(10) d. We support the previous identification of GALEX J015054.4+310745 as an sdB star and provide physical parameters for the star from spectral modelling. We identify its undetected companion as a likely He white dwarf. Based on this information, we find it unlikely that Fr 2-22 is a true planetary nebula. In addition, the central star of the true planetary nebula Hen 2-84 is found to be a photometric variable, likely due to the irradiation of a cool companion. The system has an orbital period of 0.485645(30) d. We discuss limits on binary parameters based on the available light-curve data. Hen 2-84 is a strongly shaped bipolar planetary nebula, which we now add to the growing list of axially or point-symmetric planetary nebulae with a close binary central star.