The small-signal differential gain was calculated from the measured average cw and Kerr lens mode-locked (KLM) output powers over the least-misalignment-sensitive region of a completely soft-aperturing, self-starting KLM Ti:sapphire laser. The results indicate that the self-starting condition is reached with this laser operating near the center of the stable range. The simulated location of maximum differential gain and pulse buildup process show good agreement with the experimental results.