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An analytic function f with Schwarzian norm∥ 𝒮 f∥≤ 2 (1+ δ 2) is shown to satisfy a pair of two-point distortion conditions, one giving a lower bound and the other an upper bound for the deviation. Conversely, each of these conditions is found to imply that∥ 𝒮 f∥≤ 2 (1+ δ 2). Analogues of the lower bound are also developed for curves in ℝ n and for canonical lifts of harmonic mappings to minimal surfaces.