  We examine the growing data set of binary millisecond pulsars that are
thought to have a helium white dwarf companion. These systems are believed to
form when a low- to intermediate-mass companion to a neutron star fills its
Roche lobe between central hydrogen exhaustion and core helium ignition. We
confirm that our own stellar models reproduce a well-defined period-companion
mass relation irrespective of the details of the mass transfer process. With
magnetic braking this relation extends to periods of less than 1d for a 1Msun
giant donor. With this and the measured binary mass functions we calculate the
orbital inclination of each system for a given pulsar mass. We expect these
inclinations to be randomly oriented in space. If the masses of the pulsars
were typically 1.35Msun then there would appear to be a distinct dearth of
high-inclination systems. However if the pulsar masses are more typically 1.55
to 1.65Msun then the distribution of inclinations is indeed indistinguishable
from random. If it were as much as 1.75Msun then there would appear to be an
excess of high-inclination systems. Thus with the available data we can argue
that the neutron star masses in binary millisecond pulsars recycled by mass
transfer from a red giant typically lie around 1.6Msun and that there is no
preferred inclination at which these systems are observed. Hence there is
reason to believe that pulsar beams are either sufficiently broad or show no
preferred direction relative to the pulsar's spin axis which is aligned with
the binary orbit. This is contrary to some previous claims, based on a subset
of the data available today, that there might be a tendency for the pulsar
beams to be perpendicular to their spin.
