The contribution of this article is to propose and experimentally validate an optimizing control strategy for power kites flying crosswind. The control strategy provides both path control (stability) and path optimization (efficiency). The path following part of the controller is capable of robustly following a reference path, despite significant time delays, using position measurements only. The path-optimization part adjusts the reference path in order to maximize line tension. It uses a real-time optimization algorithm that combines off-line modeling knowledge and on-line measurements. The algorithm has been tested comprehensively on a small-scale prototype, and this article focuses on experimental results.