A modification of rank priority arbitration for access to computer system resources through a shared pipeline that provides more equitable arbitration by allowing a higher ranked request access to the shared resource ahead of a lower ranked requester only one time. If multiple requests are active at the same time, the rank priority will first select the highest priority active request and grant it access to the resource. It will also set a ‘blocking latch’ to prevent that higher priority request from re-gaining access to the resource until the rest of the outstanding lower priority active requesters have had a chance to access the resource.