When a thread of program execution on a computer system is executing a critical code section, i.e., a code section whose preemption could result in inconsistency, it asserts an indicator of that fact. When the system's scheduler reschedules the thread for execution, it determines whether the indicator is asserted. If the indicator is asserted, the scheduler does not cause the thread immediately to resume execution where the thread left off when it was preempted. Instead, the scheduler has the thread's signal handler execute in such a manner that the thread performs inconsistency-avoiding operations.