Let S be the usual class of univalent analytic functions/on [z\\z\ < 1) normalized by/(z) m z + a2z2 + -■ • . We prove that the functions which are support points of C, the subclass of S of close-to-convex functions, and extreme points of DC(2, are support points of S and extreme points of DCS whenever 0 < |arg(-jc/>>)| < ir/4. We observe that the known bound of it/A for the acute angle between the omitted arc of a support point of S and the radius vector is achieved by the functions f with |arg(-x/^)| -ir/4.