Various embodiments of the present invention are directed to methods by which a virtual-machine monitor can introduce branch instructions, in order to emulate privileged and other instructions on behalf of a guest operating system, into guest-operating-system code residing on virtually aliased virtual-memory pages. In a described embodiment of the present invention, the virtual-machine monitor physically aliases each virtual alias for a particular physical memory page by allocating a physical page for the virtual alias, copying the original contents of the physical memory page to the allocated physical page, or physical alias page, and subsequently patching each physical alias page appropriate to the physical address of the physical alias page.