Transient scattering by smooth concave-convex targets reveals certain features that cannot be interpreted as conventional specular reflection and creeping wave contributions. The explanation can be found with an extended ray theory that includes complex specularly reflected incident and creeping rays in addition to the conventional real rays, and furnishes quantitatively accurate values for the scattered field when the incident pulse has a weak low-frequency spectrum. The theory has been tested previously on a periodically deformed cylinder. Now, the cylindrical test object is peanut shaped. The excellent agreement between the extended ray solution and a numerical reference solution serves as further confirmation of the validity and utility of the extended ray technique for quantitative treatment of scattering from smooth convex-concave shapes.