The "double-end" free-energy perturbation (DEFEP) expression, as the Taylor expansions show, presents an asymptotic solution for Bennett's acceptance ratio (BAR) method at large energy gaps. Iterative self-consistent calculations for solving the BAR equation oscillate between two energy values in such a case, and only using the DEFEP result as a first-guess yields formal convergence of the self-consistence procedure. The DEFEP estimate also provides a good starting point for the iterative procedure of BAR for the whole range of state overlap. Microscopic force field molecular dynamics simulations of the hydration free energies for transformation O(+)-->O(-) support these data. The simulations also prove robustness of the multistage perturbation schemes as compared with single-stage calculations. The observed difference between the BAR and DEFEP results has a maximum at intermediate values of energy gaps and is getting smaller for energy gaps less than 10-15 kT.