This paper examines the problem of simultaneously optimizing the spooling and cross-current flight trajectory of a tethered marine hydrokinetic kite using an analytic solution of its inverse dynamics. Tethered kites hold considerable promise for energy production, especially when undergoing cross-current motion. The novelty of this work lies in the use of an analytic solution of the inverse dynamics of the kite to solve the trajectory optimization problem. The term “inverse dynamics” refer to the process of obtaining an exact solution for the actuator inputs from the position, velocity, and acceleration of the kite. While the literature on tethered kites explores trajectory optimization in great detail, most of the work exploits the forward dynamics of the kite, and does not simultaneously optimize the spooling motion and cross-current trajectory. This paper formulates the co-optimization of the kite spooling and cross-current trajectory using a three degrees-of-freedom kite model, paired with an inelastic tether model. The analytic solution of the inverse dynamics is solved in terms of the roots of a fourth-order polynomial in terms of the angle of attack. A simulation study validates the optimization approach and shows that the kite is able to achieve significant energy production.