An alternative approach for treating strongly interacting statistical systems with strongly singular potentials is developed. This approach combines both the advantages of decoupling procedures for Green functions, which eliminate divergences caused by singular potentials, and the advantages of perturbation theory, which is a regular procedure that makes it possible to construct subsequent approximations above the chosen decoupling. The resulting iterative sequence of Green functions generates corresponding sequences of observable quantities. To improve the convergence of the latter sequences a method is suggested based on the renormalization-group ideas. A simple illustration is given.