A hybrid model is proposed in order to exploit the idea of compensating semiconductor optical amplifiers (SOAs) nonlinearity by adjusting cavity dispersion in a SOA-fiber ring mode-locked laser. The model is checked by analytical as well as experimental results. Excellent agreement is obtained in both cases. It is predicted that, once the cavity dispersion is correctly adjusted, the mode-locked pulses of 10 ps width will become distortion-free Gaussians, with their time-bandwidth product (TB) very close to the fundamental Gaussian limit (TB = 1/2) using root-mean-square definition. We will show evidence and explain why other waveforms, notably soliton, are highly unlikely in such a system. Some interesting effects related to band-pass filter are revealed as well. Our results highlight the ambiguity of TB using full-width at half-maximum (FWHM) definition. As a consequence, the widely adopted notion of transform-limited pulse in its FWHM version might be misleading.