This paper shows the possibility of obtaining fast, but still adiabatic, amplification of soliton pulses by using a rapidly increasing distributed amplification with scale lengths comparable with the characteristic dispersion length. Explicit expressions for the required distribution of this gain and the variation of the pulse width are given, and theoretical predictions have been verified by numerical simulations. The practical implementation of the compression scheme should be possible by using an active fiber with a doping proportional to the required gain distribution. A study was also made of how efficient compression of solitons can be obtained.