Large numbers of precision fusion excitation functions were fitted in the literature using the nucleus-nucleus interaction potential having the Woods-Saxon shape. The diffuseness of this potential fusion ranges from 0.75 to 1.5 fm. This is much larger than the value of 0.65 fm required by the elastic scattering data. Trying to resolve this contradiction we develop the dissipative trajectory model based on the density-dependent M3Y NN-forces folded with the nuclear matter distribution. Resulting potential possesses the normal diffuseness about 0.65 fm. With this potential we reach the agreement with the data for ¹⁶O+²⁰8Pb, ²⁸Si+²⁰⁸Pb, ³²S+²⁰⁸Pb reactions within 5%.