It is known that if a Banach space Y is a u-ideal in its bidual Y** with respect to the canonical projection on the third dual Y*** , then Y* contains “many” functionals admitting a unique norm-preserving extension to Y**—the dual unit ball BY* is the norm-closed convex hull of its weak* strongly exposed points by a result of A. Lima from 1995. We show that if Y is a strict u-ideal in a Banach space X with respect to an ideal projection P on X* , and X/Y is separable, then BY* is the τP-closed convex hull of functionals admitting a unique norm-preserving extension to X, where τP is a certain weak topology on Y* defined by the ideal projection P.