The principal existence theorem (i.e., Theorem 1) of "Existence and behavior of the radial limits of a bounded capillary surface at a corner" (Pacific J. Math. 176:1 (1996), 165-194) is extended to the case of a contact angle gamma which is not bounded away from 0 and pi (and depends on position in a bounded domain Omega is an element of R-2 with a convex corner at O = (0, 0)). The lower bound on the size of "side fans"(i.e., Theorem 2 in the above paper) is extended to the case of such contact angles for convex and nonconvex corners.