Precision tuning is an approximate computing technique for trading precision with lower execution time, and it has been increasingly important in embedded and high-performance computing applications. In particular, embedded applications benefit from lower precision in order to reduce or remove the dependency on computationally-expensive data types such as floating point. Amongst such applications, an important fraction are mission-critical tasks, such as control systems for vehicles or medical use-cases. In this context, the usefulness of precision tuning is limited by concerns about verificability of real-time and quality-of-service constraints. However, with the introduction of optimisations techniques based on integer linear programming and rigorous WCET (Worst-Case Execution Time) models, these constraints not only can be verified automatically, but it becomes possible to use precision tuning to automatically enforce these constraints even when not previously possible. In this work, we show how to combine precision tuning with WCET analysis to enforce a limit on the execution time by using a constraint-based code optimisation pass with a state-of-the-art precision tuning framework.