  The loss of angular momentum due to unstable r-modes in hot young neutron
stars has been proposed as a mechanism for achieving the spin rates inferred
for young pulsars. One factor that could have a significant effect on the
action of the r-mode instability is fallback of supernova remnant material. The
associated accretion torque could potentially counteract any gravitational-wave
induced spin-down, and accretion heating could affect the viscous damping rates
and hence the instability. We discuss the effects of various external agents on
the r-mode instability scenario within a simple model of supernova fallback on
to a hot young magnetized neutron star. We find that the outcome depends
strongly on the strength of the star's magnetic field. Our model is capable of
generating spin rates for young neutron stars that accord well with initial
spin rates inferred from pulsar observations. The combined action of r-mode
instability and fallback appears to cause the spin rates of neutron stars born
with very different spin rates to converge, on a timescale of about a year. The
results suggest that stars with magnetic fields $\le10^{13}$ G could emit a
detectable gravitational wave signal for perhaps several years after the
supernova event. Stars with higher fields (magnetars) are unlikely to emit a
detectable gravitational wave signal via the r-mode instability. The model also
suggests that the r-mode instability could be extremely effective in preventing
young neutron stars from going dynamically unstable to the bar-mode.
