The self-frequency shift (SFS) resulting from Raman self-pumping effect of optical soliton and amplifer spontanious emission (ASE) noise produced in the amplification of optical soliton can both be reduced significantly by making amplifer gain depend on soliton frequency. In this paper, the above two schemes are investigated analytically and numerically by using pertubation method of inverse scattering theory and the concept of fouier transform an ensemble average. The result shows that the two schemes are effective in controlling ASE noise hence the limitation of G-H effect can be weakened obviously. The comparison with results of computer similation is made.