Aerodynamic issues are discussed in the design of an optimum contra-rotating coaxial helicopter rotor system. The approaches needed to make profitable rotor design changes to improve performance in both hovering and forward flight are described. As a result of rotor-on-rotor flow interference effects, and becase a coaxial rotor system must generally operate at a torque-balanced condition, the upper and lower rotors are shown to encounter significantly different aerodynamic conditions, especially in hovering flight. A general design goal for maximizing performance is to minimize the combined sources of losses on the upper and lower rotors, particularly those resulting from aerodynamic interference. Parametric studies were conducted to study the effects of changing interrotor spacing, blade twist rates, and blade planform, on the interdependent loads produced on the upper and lower rotors, respectively. A formal, multi-step optimization process was then conducted by coupling a free-vortex wake method with an optimization algorithm based on the method of feasible directions. The goal was to quickly find the best blade geometry to give the highest rotor figure of merit in hover and/or the minimum power required in forward flight. Because of the inherent aerodynamic differences at each rotor, an optimum performing coaxial rotor is shown to require different blade shapes (i.e., with different twists and planforms) on the upper and lower rotors. Furthermore, because of the differential thrust sharing on the rotors, it is shown that to maximize the stall margins, the upper rotor of the pair must have a higher value of solidity. While the coaxial rotor optimization problem is shown to be nonconvex, the present study confirms that rotor efficiency can be increased by striving to find the optimum distributions of blade twist and planform, even though the two rotors may ultimately end up with different blade shapes.