We investigate the optimal design of a compound helicopter comprised of counter-rotating coaxial rotors, a propeller, and optionally a fixed wing. We determine the blade geometry, azimuthal blade pitch inputs, optimal shaft angle (rotor angle of attack), and division of propulsive and lifting forces among the components that minimize the total power for a given flight condition. The optimal design problem is cast as a variational statement that minimizes the sum of induced and viscous power losses for a prescribed lift, propulsive force, and vehicle trim condition. The rotor, propeller, and wing geometry and control inputs are related to the far-field circulation through a lifting line model that accounts for experimentally or computationally determined nonlinear lift and drag polars. The variational statement is discretized using a vortex lattice wake, and the resulting nonlinear constrained optimization problem is solved via Newton iteration. We show that varying the prescribed propulsive force of the system affects the optimal shaft angle and rotor design, and that higher harmonic control reduces total vehicle power loss (inefficiency) in high speed flight by as much as 15 percent. We also show that imposing a maximum allowable lateral lift offset can greatly increase the power loss of the coaxial rotors. © 2014 by the American Helicopter Society International, Inc. All rights reserved.