We present results of the Canada-France-Hawaii Telescope adaptive optics (AO) search for companions of a homogeneous group of contact binary stars, as a contribution to our attempts to prove the hypothesis that these binaries require a third star to become as close as observed. In addition to directly discovering companions at separations of >=1'', we introduced a new method of AO image analysis utilizing distortions of the AO diffraction ring pattern at separations of 0.07''-1''. Very close companions, with separations in the latter range, were discovered in the systems HV Aqr, OO Aql, CK Boo, XY Leo, BE Scl, and RZ Tau. More distant companions were detected in V402 Aur, AO Cam, and V2082 Cyg. Our results provide a contribution to the mounting evidence that the presence of close companions is a very common phenomenon for very close binaries with orbital periods <1 day.