We discuss in detail a compact all-solid-state laser delivering sub-5-fs, 2-MW pulses at repetition rates up to 1 MHz. The shortest pulse generated thus far measures only 4.6 fs. The laser system employed is based on a cavity-dumped Ti:sapphire oscillator whose output is chirped in a single-mode fiber. The resulting white-light continuum is compressed in a novel high-throughput prism chirped-mirror Gires-Tournois interferometer pulse compressor. The temporal and spectral phase of the sub-5-fs pulses are deduced from the collinear fringe-resolved autocorrelation and optical spectrum. The derived pulse shape agrees well with the one retrieved from the measured group delay of the continuum and calculated characteristics of the pulse compressor.