  This is the third of a series of papers that presents an algorithm to search
for close binaries with massive, possibly compact, unseen secondaries. The
detection of such a binary is based on identifying a star that displays a large
ellipsoidal periodic modulation, induced by tidal interaction with its
companion. In the second paper of the series we presented a simple approach to
derive a robust modified minimum mass ratio (mMMR), based on the observed
ellipsoidal amplitude, without knowing the primary mass and radius, assuming
the primary fills its Roche lobe. The newly defined mMMR is always smaller than
the actual mass ratio. Therefore, a binary with an mMMR larger than unity is a
good candidate for having a massive secondary, which might be a black hole or a
neutron star. This paper considers 10,956 OGLE short-period ellipsoidals
observed towards the Galactic Bulge. We re-analyse their modulation and
identify 136 main-sequence systems with mMMR significantly larger than unity as
candidates for having compact-object secondaries, assuming their observed
periodic modulations reflect indeed the ellipsoidal effect. Obviously, one
needs follow-up observations to find out the true nature of these companions.
