Results: For fine-to-medium grains on Silicon Graphics GTX/LLI) (SGI), the parallel heap yields ab- solute speedups of two to four using six processors with increasing granularity (max Think varying from 1 to 4000) on a heap of size n = 102411 ’items while processing T = 13K items in each delete-think-insert cycle (a concurrency factor of less that 1%). These speedups are significantly more than those obtained from the other two data structures. Almost similar speedups are maintained for smaller concurrency factors (for T > 128). Even for smaller priority queues, the parallel heap is either better than or at par with the others. For very small n, or for coarser grain, the serial heap outperforms others. The concurrent heap did not show any superiority over serial heap under these test conditions. The paper’s organization is as follows: Section 2 briefly describes each of the three data structures and their operations. Section 3 describes the implementation details of various heaps and their performance tune-ups. Section 4 contains experimental configurations and the timing plots comparing the three data structures. Section 5 contains some concluding re- marks.