In the present paper, the problem of one-dimensional screening photorefractive solitons is reconsidered in the context of the accordance of soliton solutions with the Kukhtarev–Vinetskii model. In all theoretical and experimental works dealing with the analysis of such type solitons, one assumes that under the slowly varying approximation for the optical field amplitude the reduced form of photorefractive rate equations can be employed. In this work, we point out that the crucial and commonly accepted approximation within this scheme has a limited range of applicability as regards dark solitons. This author proposes a relatively simple modification of the standard saturable photorefractive response formula to obtain the plausible self-consistent solutions. The improved solutions for screening black solitons have been derived and discussed by comparison with standard solutions.