We consider evolutionary models for the population of short-period ( ¡10 hr ) low-mass black-hole binaries ( LMBHBs ) and compare them with observations of soft X-ray transients ( SXTs ) . We show that assuming strongly reduced magnetic braking ( as suggested by us before for low-mass semidetached binaries ) the calculated masses and effective temperatures of secondaries are encouragingly close to the observed masses and effective temperatures ( as inferred from their spectra ) of donor stars in short-period LMBHBs . Theoretical mass-transfer rates in SXTs are consistent with the observed ones if one assumes that accretion discs in these systems are truncated ( “ leaky ” ) . We find that the population of short-period SXTs is formed mainly by systems which had unevolved or slightly evolved main-sequence donors ( M _ { 2 } \lesssim 1.2 M _ { \odot } ) with a hydrogen abundance in the center X _ { c } > 0.35 at the Roche-lobe overflow ( RLOF ) . Longer period ( 0.5 - 1 ) day ) SXTs might descend from systems with initial donor masses of about 1 M _ { \odot } and X _ { c } < 0.35 . Thus , one can explain the origin of short period LMBHB without invoking donors with cores almost totally depleted of hydrogen . Our models suggest that , unless the currently accepted empirical estimates of mass-loss rates by winds for massive O-stars and Wolf-Rayet stars are significantly over-evaluated , a very high efficiency of common-envelope ejection is necessary to form short-period LMBHBs .