This work studies length-minimizing arcs in sub-Riemannian manifolds \((M, E, G)\) where the metric \(G\) is defined on a rank-two bracket-generating distribution \(E\). The authors define a large class of abnormal extremals—the “regular” abnormal extremals—and present an analytic technique for proving their local optimality. If \(E\) satisfies a mild additional restriction-valid in particular for all regular two-dimensional distributions and for generic two-dimensional distributions—then regular abnormal extremals are “typical,” in a sense made precise in the text. So the optimality result implies that the abnormal minimizers are ubiquitous rather than exceptional.