  A strongly relativistic binary pulsar has been recently discovered with the
64m Parkes telescope (Burgay et al. 2003). Here we use the measured properties
of this binary (masses and orbital characteristics as well as age estimates),
and we derive the complete set of constraints imposed on the physical
properties of the binary pulsar progenitor right before the second supernova
explosion. We find that: (i) according to our current understanding of
neutron-star formation, the helium-rich progenitor of the second neutron star
is most likely overflowing its Roche lobe; (ii) the neutron-star kick magnitude
is constrained in the range 60-1560 km/s, with the most probable value being
equal to 150 km/s. While the first conclusion is in agreement with Dewi & van
den Heuvel (2003), our upper limit on the kick magnitude is significantly
larger than that derived by these authors. We find that the difference arises
because Dewi & van den Heuvel (2003) inadvertently neglected to consider kicks
directed out of the pre-supernova orbital plane.
