Multiple-kite airborne wind energy (AWE) systems are typically characterized by unstable and highly non-linear dynamics which often translates to intricate controller design and challenging coordination problems. Rotary kite AWE systems (RAWES) have been alternatively proposed for small-scale applications, under the assumption that they can reduce the complexity of the control problem. This paper confirms that a small, rigid-wing RAWES in pumping mode can be controlled effectively in a large operational range, using only pitch control as on-board actuation. Optimal control is applied to compute RAWES pumping trajectories in different operating regions, for a design geometry that is optimized for a rated wind speed under structural constraints. The reduced control complexity comes at the cost of a low harvesting factor, close to that of conventional wind turbines.