When a probe pulse copropagates with a pump pulse inside an optical fiber, the two can interact through cross-phase modulation. It is shown that an interplay between the effects of group-velocity dispersion and cross-phase modulation can lead to optical wave breaking that manifests as rapid oscillations near the leading or the trailing side of the probe pulse. Qualitative features of this new kind of optical wave breaking are discussed, as well as the conditions under which it can be observed experimentally. The probe pulse can be compressed significantly by optimizing the initial delay between the pump and probe pulses even when the two pulses experience normal dispersion in the fiber.