Irregular computation problems underlie many important scientific applications. Although these problems are computationally expensive, and so would seem appropriate for parallel machines, their irregular and unpredictable run-time behavior makes this type of parallel program difficult to write and adversely affects run-time performance. This paper explores three issues---partitioning, mutual exclusion, and data transfer---crucial to the efficient execution of irregular problems on distributed-memory machines. Unlike previous work, we studied the same programs running in three alternative systems on the same hardware base (a Thinking Machines CM-5): the CHAOS irregular application library, Transparent Shared Memory (TSM), and eXtensible Shared Memory (XSM). CHAOS and XSM performed equivalently for all three applications. Both systems were somewhat (13%) to significantly faster (991%) than TSM.