The described embodiments relate to a processor that speculatively executes instructions. During operation, the processor often executes instructions in a speculative-execution mode. Upon detecting an impending pipe-clearing event while executing instructions in the speculative-execution mode, the processor stalls an instruction fetch unit to prevent the instruction fetch unit from fetching instructions. In some embodiments, the processor stalls the instruction fetch unit until a condition that originally caused the processor to operate in the speculative-execution mode is resolved. In alternative embodiments, the processor maintains the stall of the instruction fetch unit until the pipe-clearing event has been completed (i.e., has been handled in the processor).