Relating the λσ- and λs-styles of explicit substitutions

Two methods of explicit substitutions, ?s- and ?s-styles, are compared. A criterion of adequacy is used to simulate ß-reduction in calculi of explicit substitutions and apply it to several calculi: ?s; ?s_?; ?v; ?s; ?t; and ?u. Results proved that ?t is more adequate than ?v and that ?u is more adequate that ?v, ?s_?, and ?s. Counterexamples is given to show that all other comparisons are impossible according to the criterion.