A processing pipeline for processing instructions with instructions from multiple threads in flight concurrently may have control circuitry to detect a stalling event associated with a given thread. In response, at least one instruction of the given thread may be flushed from the pipeline, and the control circuitry may trigger fetch circuitry to reduce a fraction of the fetched instructions which are fetched from the given thread. A mechanism is also described to determine when to trigger a predetermined action when a delay in accessing information becomes greater than a delay threshold, and to update the delay threshold based on a difference between a return delay when the information is returned from the storage circuitry and the delay threshold.