We report the generation and measurement of 804 nm pulses with durations as short as 20 fs and with peak powers as high as 500 kW from a regeneratively initiated, self-mode-locked Ti:sapphire laser. Pulse duration is shown to decrease, and spectral content to increase, as intracavity power is increased. Control of intracavity focusing and a high-modulation-depth, acousto-optic modulator allow the intracavity power to be maximized. Cavity cubic phase error is minimized by correct design and placement of a GDD compensating prism pair. Methods for accurate determination of the pulse duration without assumption of pulse shape are discussed. Interferometric autocorrelation is accomplished with an interferometer which intrinsically balances dispersion and loss in each arm. Techniques for eliminating pulse distortions during amplification are also presented.