Path reduction is a well-known technique to alleviate the state-explosion problem incurred by explicit-state model checking, its key idea being to store states only at predetermined breaking points. This paper presents an adaptation of this technique which detects breaking points on-the-fly during state-space generation. This method is especially suitable for the detection of breaking points in systems where static analyses yield coarse over-approximations. We evaluate the effectiveness of this technique by applying it to binary code verification.