In a computational grid environment, a common practice is try to allocate an entire parallel job onto a single participating site. Sometimes a parallel job, upon its submission, cannot fit in any single site due to the occupation of some resources by running jobs. How the job scheduler handles such situations is an important issue which has the potential to further improve the utilization of grid resources as well as the performance of parallel jobs. This paper develops adaptive processor allocation methods based on the moldable property of parallel jobs to deal with such situations in a heterogeneous computational grid environment. The proposed methods are evaluated through a series of simulations using real workload traces. The results indicate that adaptive processor allocation methods can further improve the system performance of a load sharing computational grid.