A grid has to provide strong incentive for participating sites to join and stay in it. Participating sites are concerned with the performance improvement brought by the gird for the jobs of their own local user communities. Feasible and effective load sharing is key to fulfilling such a concern. This paper explores the load-sharing policies concerning feasibility and heterogeneity on computational grids. Several job scheduling and processor allocation policies are proposed and evaluated through a series of simulations using workloads derived from publicly available trace data. The simulation results indicate that the proposed job scheduling and processor allocation policies are feasible and effective in achieving performance improvement on a heterogeneous computational grid.