In this work, the overall perceived pitch (principal pitch) of pure tones modulated in frequency with an asymmetric waveform is studied. The dependence of the principal pitch on the degree of asymmetric modulation was obtained from a psychophysical experiment. The modulation waveform consisted of a flat portion of constant frequency and two linear segments forming a peak. Consistent with previous results, significant pitch shifts with respect to the time-averaged geometric mean were observed. The direction of the shifts was always toward the flat portion of the modulation. The results from the psychophysical experiment, along with those obtained from previously reported studies, were compared with the predictions of six models of pitch perception proposed in the literature. Even though no single model was able to predict accurately the perceived pitch for all experiments, there were two models that give robust predictions that are within the range of acceptable tuning of modulated tones for almost all the cases. Both models point to the existence of an underlying "stability sensitive" mechanism for the computation of pitch that gives more weight to the portion of the stimuli where the frequency is changing more slowly.