We present a model for the spindown of young radio pulsars in which the neutron star loses rotational energy not only by emitting magnetic dipole radiation but also by torquing a surrounding accretion disk produced by supernova fallback. The braking index predicted in our model is in general less than n=3 (the value for pure dipole magnetic radiation), in agreement with the reported values of n<3 for five young radio pulsars. With an accuracy of 30% or better, our model reproduces the age, braking index and third frequency derivative of the Crab pulsar for a disk accretion rate in the range 3 x 10^16 - 10^17 g/s.
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