One of many examples: Project Azorian

During the Cold War the Soviets lost a nuclear submarine in international waters. The Soviets couldn't find it, the US (through its network of acoustic listening stations in the oceans) could. There was a multi-year effort to recover the sub, which required an elaborate cover story and operational security.

If the Soviets knew what the recovery ship was doing, they would have blown it out of the water. All the secrecy was necessary to protect the mission.