In many systems, there are peripherals or data elements that must only be accessed by a single task at a time. The obvious way to enforce exclusive access to such resources is through a mutual exclusion semaphore (“mutex”). However, this may lead to a scenario termed priority inversion, whereby a higher priority task is indirectly blocked by a lower priority one. This paper examines the problem and details the available remedies, and introduces novel approaches for dynamic priority tracking, optimal priority demotion, adaptive priority ceiling, orphan mutex protection, and automatic deadlock detection.