We present a detailed investigation of Kerr-lens mode-locking in diode-pumped Cr:LiSAF lasers employing gain-matched output couplers (GMOCs). Single-mode diodes (660 nm, 130 mW) and tapered diodes (685 nm, 1 W) were investigated as diode pump sources. We have shown that, by reducing the gain-filtering effect, GMOC enhances the effective self-amplitude modulation depth and provides a significant improvement in both efficiency and robustness of KLM operation. From the single-mode diode pumped system, 13 fs pulses with an average power of 25 mW and a peak power 25 kW have been generated at an incident pump power of only 120 mW (21% optical-to-optical conversion efficiency). The tapered diode pumped Cr: LiSAF oscillator provided pulses as short as 14.5 fs with 106-mW average power and 60-kW peak power at an incident pump power of 940 mW (11% optical-to-optical conversion efficiency). A femtosecond tuning range extending from 807 to 919 nm was also realized with sub-50-fs long pulses. To our knowledge, demonstrated optical-to-optical conversion efficiencies, peak powers and fs tuning ranges are record results for Cr: LiSAF laser oscillators. The obtainable pulsewidth and fs tuning range are currently limited by the dispersion/reflectivity bandwidth of the available optics.