Fuel-optimal rendezvous in orbit is examined using thrust-impulses and coasting arcs. Necessary conditions for the optimality of fuel-optimal rendezvous with and without radial constraints are derived. These conditions are then used to verify the optimality of trajectories obtained from a parameter-optimization technique. For rendezvous problems with radial constraint, locally optimal trajectories include constrained arcs or touch-point arcs. Numerical procedures to compute the costates and the jumps in the costates at the touch point and at the entry point to the constraint arc are provided. Locally optimal solutions for non-optimal trajectories with a minimum radius-constraint are obtained using criteria due to Lion and Handelsmann. Numerical solutions show that multiple-impulse trajectories almost always result in a lower cost function than the corresponding two impulse trajectories. It is also observed that trajectories comprised of only touch-point arcs can often be improved by using an additional impulse. / M. S.