Motivated by the challenging crossing of the 1: 1 resonance planned for the Dawn mission a general transfer design strategy is developed using the manifold structure of near-synchronous, unstable periodic orbits. Two families of transfers across the 1: 1 resonance at the asteroid Vesta demonstrate the approach. A family of low-inclination low-energy transfers follows the stable and unstable manifolds of the libration orbits near Vesta's equilibrium points (in a surface-fixed rotating frame). A high-inclination family of transfers arises similarly from the manifold structure of near-polar near-circular orbits. Ballistic resonance crossing transfers near Vesta are presented and characterized. This transfer design methodology applies well to any solar system body where the dynamics are dominated by gravitational acceleration from a nonspherical central-body potential. Copyright © 2012 by the authors.