A technique for significantly suppressing severe fourth-order dispersion of ultrashort optical pulses in long-distance transmission is analyzed by use of the quadratic phase from the excess second-order dispersion of the fiber link in conjunction with synchronously applied cosine phase modulation of temporally stretched pulses. Numerical simulation predicts much improved transmission of 250-fs pulses at 5-10-GHz repetition rates over ~100 km of fiber by pi-3.5pi phase modulation.