Which situation is NOT given first priority by air traffic controllers?

An aircraft declaring minimum fuel is a situation that, while serious, does not receive the same level of immediate priority as an emergency or mechanical failure. When an aircraft declares an emergency, it indicates an urgent situation that may endanger the safety of the aircraft and those on board, warranting prompt assistance and priority handling from air traffic controllers. Similarly, a mechanical failure poses significant risks that necessitate quick and decisive action to ensure the aircraft's safe landing.

In contrast, while minimum fuel is critical and requires timely handling, it indicates that the aircraft is low on fuel but does not constitute an emergency by itself. It allows for some level of operational discretion and does not typically require as immediate action as the other situations mentioned. Therefore, it’s prioritized lower than emergencies or failures in air traffic control protocols.