An indirect optimization method is used to find optimal trajectories that use solar electric propulsion. Missions that exploit variable specific impulse are compared to constant-specific-impulse trajectories, and the benefit, in terms of payload, is highlighted. The presence of limits on the attainable values of the specific impulse and the use of dual-mode thrusters, which operate only at two discrete values of specific impulse, are also considered. The analytical formulation of the problem is presented, and the necessary conditions for an optimal solution are discussed. Numerical examples deal with planet rendezvous missions; a Mercury mission would largely benefit from the management of the available power, which exhibits a tenfold variation caused by the vehicle's varying distance from the sun. The optimization method can also deal with planetary gravity assists; Mercury missions, which exploit Venus flybys, are optimized and their characteristics discussed. Results show that the dual-mode thrusters provide almost the same propellant savings as the more complex variable-specific-impulse thrusters.