Holographic grating recording efficiency and their coherent self-enhancement efficiency are experimentally studied depending on the recording light intensity modulation index (interference fringe visibility) in an a-As2S3 chalcogenide film in order to find the minimum modulation.Theoretical analysis of the obtained results is made. The minimum light intensity modulation index Mmin=3.6×10-4 is found which is determined by the scattered light background.In this case the maximal diffraction ηmax was 0.006% and the maximal self-enhancement factor max was 2.45 compared with ηmax =15%, max = 11.8 in the optimal M=1.000 case. In the case of two-beam holographic grating recording the maximal diffraction efficiency increases when M is increased whereas sensitivity decreases.The former is due to the nonlinearity of material response, and the latter can be explained by the recording light intensity dependence. In the case of coherent self-enhancement both the maximal diffraction efficiency and sensitivity increase with the recording modulation index M. This can be explained by mechanical stress modulation during the initial grating recording depending on M followed by relaxational structural changes enhancing coherent self-enhancement effect .The existence of coherent-self enhancement effect is determined by the competition of excitation and relaxation processes rather than by a minimum modulation. The existence condition of the grating coherent self-enhancement is found.