For any odd integer d ≥ 3, we determine the sharpest constant Cp;q;r such that ∥XY − Y X∥p ≤ Cp;q;r∥X∥q∥Y ∥r for all X; Y ∈ Md; where Md denotes the set of all d×d complex matrices, ∥·∥p, 1 ≤ p ≤ ∞, denotes the Schatten p-norm on Md, and 1 ≤ p; q; r ≤ ∞satisfy 1 p > 1 q+1 r . This is a continuation of the study of the problem considered in [D. Wenzel and K. Audenaert, Impressions of convexity: an illustration for commutator bounds, Linear Algebra Appl., vol. 433 (2010), pp. 1726–1759.]