In various embodiments of the present invention, a virtual monitor can arrange to properly emulate execution of a cover instruction by operating-system code, or other code assuming to run at highest privilege level, by monitoring a window of instruction execution in which a cover instruction may be executed. Upon occurrence of an interruption, the virtual monitor may configure performance monitoring by the IA-64 processor to count the number of times a cover instruction is executed. When a subsequent attempt is made by a routine executing at a privilege level lower than the highest privilege level to read the contents of a special control register into which the contents of the CFM register would have been stored had a cover instruction been executed under conditions obtainable only to code running at the highest privilege level, the virtual monitor can determine whether or not a cover instruction was, in fact, executed by the non-privilege routine and can properly emulate access to the special control register by the routine running at less than highest privilege level. In alternative embodiments, other non-privileged instructions that behave different depending on the privilege level of the processor at the time they execute can be virtualized by the virtualization technique used for the cover instruction.