Propagation of femtosecond light pulses in water is investigated. By changing input power from slightly above to highly above threshold for self-focusing, it is shown that either group velocity dispersion (GVD) or multi-photon ionization (MPI) and multi-photon absorption (MPA) may arrest the collapse. When MPI and MPA dominate the propagation, the pulse can be self-compressed to a few optical cycles. In spectral domain, MPI alone induces a strong blue shift. MPA can restrain this strong blue shift.