A data processing apparatus comprises processing circuitry arranged to process processing threads using resources accessible to the processing circuitry. A pipeline is provided for handling at least two pending threads awaiting processing by the processing circuitry. The pipeline includes at least one resource-requesting pipeline stage for requesting access to resources for the pending threads. A priority controller controls priority levels of the pending threads. The priority levels define a priority with which pending threads are granted access to resources. When a pending thread reaches a final pipeline stage, if the request resources are not yet available then the priority level of that thread is raised selectively and the thread is returned to a first pipeline stage of the pipeline. If the requested resources are available then the thread is forwarded from the pipeline.