We analyze pulse self-compression in femtosecond filaments, both experimentally and numerically. We experimentally demonstrate the compression of 45 fs pulses down to a duration of 7.4 fs at millijoule pulse energies. This sixfold compression in a self-generated filament does not require any means for dispersion compensation and is highly efficient. We compare our results to numerical simulations, providing a complete propagation model that accounts for full dispersion, pressure variations, Kerr nonlinearity and plasma generation in multiphoton and tunnel regimes. The equations are numerically integrated and allow for a quantitative comparison with the experiment. Our experiments and numerical simulations reveal a characteristic spectrotemporal structure of the self-compressed pulses, consisting of a compressible blue wing and an incompressible red pedestal. We explain the underlying mechanism that leads to this structure and examine the scalability of filament self-compression with respect to pulse energy and gas pressure.