Dynamic dispersion compensation based on non-linear self-phase modulation (SPM) in an all-fiber device is demonstrated. The basic design of the compensator is very simple, consisting only of a pre-compensating negative dispersion fiber, an optical amplifier, and a highly non-linear positive dispersion fiber. Multiple channel operation of the compensator is feasible and experimentally demonstrated. An increase of dispersion tolerance of at least a factor of 2 is shown with low penalty of less than 2 dB. Finally, device performance in a 2000 km fiber loop experiment is presented.