This thesis shows that coarse priority schemes for rationing random supply can be implemented without prior knowledge of the distribution of valuations using the VCG mechanism. Coarse priority rationing schemes are those with fewer priority classes than individuals. Coarse priority schemes are of interest because full priority schemes may not be feasible in practice and because coarse priority schemes achieve large parts of the gains from full priority schemes. Implementation of the coarser priority schemes without knowledge of the distribution of valuations is useful when offering priority for the first time, since this information may not be available. I show that with unit demand, risk neutrality and a known supply distribution, the optimal priority scheme for a given number of classes can be implemented. I provide a program to simultaneously solve for the optimal cut-offs and VCG prices given any discrete valuations and any supply distribution.