  We consider constraints on the formation of low-mass X-ray binaries
containing neutron stars (NLMXBs) arising from the presence of soft X-ray
transients among these systems. We show that in short-period systems driven by
angular momentum loss these constraints require the secondary at the beginning
of mass transfer to have a mass > 1.2 M_sun, and to be significantly
nuclear-evolved. As a consequence a comparatively large fraction of such
systems appear as soft X-ray transients even at short periods, as observed.
Moreover the large initial secondary masses account for the rarity of NLMXBs at
periods less than 3 hr. In contrast, NLMXB populations forming with large kick
velocities would not have these properties, suggesting that the kick velocity
is generally small compared to the pre-SN orbital velocity in a large fraction
of systems. We derive constraints on progenitor system parameters and on the
strength of magnetic braking.
