Binary companions to asymptotic giant branch (AGB) stars are an important aspect of their evolution. Few AGB companions have been detected, and in most cases it is difficult to distinguish between main-sequence and white dwarf companions. Detection of photometric flickering, a tracer of compact accretion discs around white dwarfs, can help identify the nature of these companions. In this work, we searched for flickering in four AGB stars suggested to have likely accreting companions. We found no signs for flickering in two targets: R Aqr and V1016 Cyg. Flickering was detected in the other two stars: Mira and Y Gem. We investigated the true nature of Mira's companion using three different approaches. Our results for Mira strongly suggest that its companion is a white dwarf.