We solve a long-standing open problem in theory of weighted inequalities concerning iterated Copson operators. We use a constructive approximation method based on a new discretization principle that is developed here. In result, we characterize all weight functions w, v, u on (0, ∞) for which there exists a constant C such that the inequalityholds for every non-negative measurable function h on (0, ∞), where p, q and m are positive parameters. We assume that p ≥ 1 because otherwise the studied inequality cannot hold for nontrivial weights, but otherwise p, q and m are unrestricted.2010 Mathematics Subject Classification. 47G10, 47B38, 26D10.