  We study the formation of low-mass black hole X-ray binaries with main
sequence companions that have formed through case C mass transfer (mass
transfer following the helium core burning phase of the black hole progenitor).
We identify these objects with the observed soft X-ray transients. Although
this scenario requires a set of fine tuned conditions, we are able to produce a
current Galactic population of about 2000 objects, in agreement with estimates
based on observations.
  The narrow interval in initial separations leading to case C mass transfer,
combined with the allowed narrow range of separations after the common envelope
evolution, constrains the common envelope efficiency in this scenario: $\lambda
\alpha_{ce} \approx 0.2-0.5$.
