We explore mode locked operation of a Ti:Sapphire laser with enhanced Kerr nonlinearity, where the threshold for pulsed operation can be continuously tuned down to the threshold for continuous-wave (CW) operation, and even below it. At the point of equality, even though a CW solution does not exist, pulsed oscillation can be realized directly from zero CW oscillation. We experimentally investigate the evolution of the mode locking mechanism towards this point and beyond it, and provide a qualitative theoretical model to explain the results.