Observations undertaken to investigate the relation of mass transfer rates to X-ray luminosities in accreting binary X-ray sources in the Galaxy are discussed. Einstein Observatory Imaging Proportional Counter observations were made of 23 binary systems selected as possibly containing a compact object. Only three of the original 17 target objects were detected as sources, plus two more among the six also found to be within Einstein IPC fields. None of the sources detected, however, shows evidence for the presence of a compact component. It is concluded that there are few, if any, binaries in which a compact star is in a low X-ray state, and that the known hard X-ray binaries constitute the entire galactic population of such objects.