In a multi-domain computer system in which several processes are running, a composite lock provides mutually exclusive access to a resource. The composite lock has a back-end component and a front-end component. The back-end component is platform-dependent and operates as a semaphore, with Wait and Signal functions. The front-end component conditionally calls the Wait and Signal functions depending on whether the lock is currently contested when a new process wishes to acquire the lock, and on whether any process is currently suspended, waiting to acquire the lock. The front-end and back-end components may execute in different domains. In the uncontested case, the invention avoids costly domain crossings. The front-end component may also include a spinning feature to further reduce the need to invoke the back-end component and cause a domain crossing. The composite lock is particularly advantageous in computer systems that include a virtual machine.