Adjustable antenna structures may be used to compensate for manufacturing variations in electronic device antennas. An electronic device antenna may have an antenna feed and conductive structures such as portions of a peripheral conductive electronic device housing member and other conductive antenna structures. The adjustable antenna structures may have a movable dielectric support. Multiple conductive paths may be formed on the dielectric support. The movable dielectric support may be installed within an electronic device housing so that a selected one of the multiple conductive paths is coupled into use to convey antenna signals. Coupling the selected path into use adjusts the position of an antenna feed terminal for the antenna feed and compensates for manufacturing variations in the conductive antenna structures that could potentially lead to undesired variations in antenna performance.