A method for enhancing concurrency in a multiprocessor computer system is described. Various tasks in a computer system communicate using commonly accessible mailboxes to access valid data from a location in the mailbox. A task holding the valid data places that data in a mailbox, and other tasks read the valid data from the mailbox. The task that inputs the valid data into the mailbox is caused to notify other tasks addressing the mailbox that the valid data is contained therein. Thus, no central coordination of mailbox access is required. Further, busy waits for valid data are minimized and the ressources of tasks and processors are used more efficiently. By coordinating several lists associated with each mailbox, conflicts in accessing data and delays in obtaining data are also minimized.