Arbitration circuitry is provided for arbitrating between requests awaiting servicing. The requests require variable numbers of resources and the arbitration circuitry permits the request to be serviced in a different order to the order in which they were received. Checking circuitry prevents a given request other than a oldest request from being serviced when a number of available resources is less than a threshold number of resources. The threshold number is varied based on the number of resources required for at least one other request awaiting servicing.