  We describe a simulation method for the accurate study of the equilibrium
freezing properties of polydisperse fluids under the experimentally relevant
condition of fixed polydispersity. The approach is based on the phase switch
Monte Carlo method of Wilding and Bruce [Phys. Rev. Lett. {\bf 85}, 5138
(2000)]. This we have generalized to deal with particle size polydispersity by
incorporating updates which alter the diameter $\sigma$ of a particle, under
the control of a distribution of chemical potential differences
$\tilde\mu(\sigma)$. Within the resulting isobaric semi-grand canonical
ensemble, we detail how to adapt $\tilde\mu(\sigma)$ and the applied pressure
such as to study coexistence, whilst ensuring that the ensemble averaged
density distribution $\rho(\sigma)$ matches a fixed functional form. Results
are presented for the effects of small degrees of polydispersity on the
solid-liquid transition of soft spheres.
