This paper investigates the synergies and trade-offs between passive aeroelastic tailoring and adaptive aeroelastic deformation of a transport composite wing for fuel burn minimisation. This goal is achieved by optimising thickness and stiffness distributions of constitutive laminates, jig-twist shape and distributed control surface deflections through different segments of a nominal “cruise-climb” mission. Enhanced aerostructural efficiency is sought both passively and adaptively as a means of aerodynamic load redistribution, which, in turn, is used for manoeuvre load relief and minimum drag dissipation. Passive shape adaptation is obtained by embedding shear-extension and bend-twist couplings in the laminated wing skins. Adaptive camber changes are provided via full-span trailing-edge flaps. Optimised design solutions are found using a bi-level approach that integrates gradient-based and particle swarm optimisations in order to tailor structural properties at rib-bay level and retrieve blended stacking sequences. Performance benefits from the combination of passive aeroelastic tailoring with adaptive control devices are benchmarked in terms of fuel burn and a payload-range efficiency. It is shown that the aeroservoelastically tailored composite design allows for significant weight and fuel burn improvements when compared to a similar all-metallic wing. Additionally, the trailing-edge flap augmentation can extend the aircraft performance envelope and improve the overall cruise span efficiency to nearly optimal lift distributions.