  We use the grid of models described in paper~I to analyse those millisecond
pulsar binaries whose secondaries have been studied optically. In particular,
we find cooling ages for these binary systems that range from $< 1 \rm Gyr$ to
$\sim \rm 15 Gyr$. Comparison of cooling ages and characteristic spin down ages
allows us to constrain the initial spin periods and spin-up histories for
individual systems, showing that at least some millisecond pulsars had
sub-Eddington accretion rates and long magnetic field decay times.
