We demonstrate a novel technique for pulse compression of few-millijoule pulses with shorter than 10 fs duration. Our technique relies on spectral broadening in a white-light filament generated in a noble gas. In this filament we observe self-compression of 45 fs pulses down to below 8 fs duration without the need for any additional dispersion compensation. Using input pulses of 5 mJ, we generate compressed pulses with up to 3.8 mJ pulse energy. Therefore this method is much more efficient than previously demonstrated compression schemes. The generated peak powers of more than 100 GW at a kilohertz repetition rate open up a perspective for compression of few-cycle pulses with energies well beyond the capacity of hollow-fiber compressors.