We address the problem of characterization of light pulses that propagate in long-haul high-bit-rate optical communication systems under strongly perturbed conditions. We show that the conventional technique for characterization of the phase and intensity profile of such pulses becomes qualitatively inconsistent when the pulse's profile is asymmetrically distorted with respect to its center of mass. We resolve these inconsistencies by partially reformulating the conventional technique by means of appropriate pulse parameters, which we call upgraded parameters, that allow a fair characterization of the intensity and phase of all types of light pulses, including those that are asymmetrically distorted. We illustrate the effectiveness of the upgraded parameters by applying them to a meticulous characterization of light pulses in a dispersion-managed optical fiber system in which third-order dispersion is acting as a strong perturbation.