A new approach to the avoidance of system deadlocks is based on the notion of promoting a process to a higher rank when a resource is allocated to it. An advantage of this method is that it can prevent the occurrence, and therefore avoid the dynamic safety test, of many unsafe allocation states. Also, an algorithm that tests how many resources can safely be allocated is easily found and the method makes it possible to attach a cost factor to resource allocation depending on the demand and the allocation test.