Methods and systems are provided for controlling an engine drive belt tensioner system in which the engine is controlled by an engine stop-start system. When the engine stop-start system decides to stop the engine, the engine drive belt tensioner system is operated so as to increase the tension in a respective drive belt to a high level during the engine stop process. This reduces the time taken for the engine to stop and will tend to reduce any tendency for reverse rotation of the engine at the end of the stop phase.