It is shown that a properly tailored, rapidly increasing gain along the distance of propagation in a monomode fiber can provide fast but still adiabatic soliton amplification and therefore high-quality one-soliton compression for fiber lengths even shorter than the characteristic dispersive length. With the variational approach an explicit expression is given for the required variation of the inhomogeneous gain, and its validity is demonstrated by comparison with direct numerical simulations that include the calculation of the pure soliton component. It is also shown by analytical and numerical perturbation analysis that the compression scheme is stable with respect to small deviations from the ideal soliton form and gain variation. Finally, it is demonstrated that efficient soliton compression can also be obtained by cascading of instantaneous optical amplifiers in an intermediate fiber with higher dispersion, where nonlinear mode conversion preserves the soliton character of the amplified pulse. The practical implementation of these compressor schemes is discussed.