  We study the evolution of a low-mass X-ray binary by coupling a binary
stellar evolution code with a general relativistic code that describes the
behaviour of the neutron star. We find that non-conservative mass transfer
scenarios are required to prevent the formation of submillisecond pulsars
and/or the collapse to a black hole. We discuss the sweeping effects of an
active magneto-dipole rotator on the transferred matter as a promising
mechanism to obtain highly non-conservative evolutions.
