  Relativistic binary pulsars, such as B1534+12 and B1913+16 are characterized
by having close orbits with a binary separation of ~ 3 R_\sun. The progenitor
of such a system is a neutron star, helium star binary. The helium star, with a
strong stellar wind, is able to spin up its compact companion via accretion.
The neutron star's magnetic field is then lowered to observed values of about
10^{10} Gauss. As the pulsar lifetime is inversely proportional to its magnetic
field, the possibility of observing such a system is, thus, enhanced by this
type of evolution. We will show that a nascent (Crab-like) pulsar in such a
system can, through accretion-braking torques (i.e. the "propeller effect") and
wind-induced spin-up rates, reach equilibrium periods that are close to
observed values. Such processes occur within the relatively short helium star
lifetimes. Additionally, we find that the final outcome of such evolutionary
scenarios depends strongly on initial parameters, particularly the initial
binary separation and helium star mass. It is, indeed, determined that the
majority of such systems end up in the pulsar "graveyard", and only a small
fraction are strongly recycled. This fact might help to reconcile theoretically
expected birth rates with limited observations of relativistic binary pulsars.
