This paper presents the work done in designing a morphing wing concept for a small experimental unmanned aerial vehicle to improve the vehicle's performance over its intended speed range. The wing is designed with a multidisciplinary design optimization tool, in which an aerodynamic shape optimization code coupled with a structural morphing model is used to obtain a set of optimal wing shapes for minimum drag at different flight speeds. The optimization procedure is described as well as the structural model. The aerodynamic shape optimization code, that uses a viscous two-dimensional panel method formulation coupled with a nonlinear lifting-line algorithm and a sequential quadratic programming optimization algorithm, is suitable for preliminary wing design optimization tasks. The morphing concept, based on changes in wing-planform shape and wing-section shape achieved by extending spars and telescopic ribs, is explained in detail. Comparisons between optimized fixed wing performance, optimal morphing wing performance, and the performance of the wing obtained from the coupled aerodynamic-structural solution are presented. Estimates for the performance enhancements achieved by the unmanned aerial vehicles when fitted with this new morphing wing are also presented. Some conclusions on this concept are addressed with comments on the benefits and drawbacks of the morphing mechanism design.