The additive x-disorder of a permutation is the sum of the absolute differences of all pairs of consecutive elements. We show that the additive x-disorder of a permutation of S(n), n ≥ 2, ranges from n − 1 to n 2 /2 − 1, and we give a complete characterization of permutations having extreme such values. Moreover, for any positive integers n and d such that n ≥ 2 and n − 1 ≤ d ≤ n 2 /2 − 1, we propose a linear-time algorithm to compute a permutation π ∈ S(n) with additive x-disorder d.