  We identify and quantify the set of constraints that neutron star-normal star
binaries must satisfy in order to become observable LMXBs. These constraints
are related to (i) the thermal and hydrostatic equilibrium of the donors, (ii)
the degree to which the mass transfer process is conservative, and (iii) the
age of the systems. They divide the parameter space of potential LMXBs in
several distinct parts, of which those that actually become LMXBs at the onset
of mass transfer occupy only a small part. Of the remainder, many become
unstable to dynamical time scale mass transfer either at the onset or later in
the course of mass transfer, and enter common envelope evolution. Others
experience super-Eddington mass transfer but may eventually survive to become
LMXBs. These survivors arguably include binary millisecond pulsars with orbital
periods in excess of $100$\,d, ultrashort-period LMXBs with hydrogen-deficient
donors, and long-period LMXBs with giant donors.
