Electronic device antenna structures may include first and second antennas. A housing may have a periphery that is surrounded by peripheral conductive structures such as a segmented peripheral metal member. A segment of the peripheral metal member may be separated from a ground by an opening. An antenna feed for the first antenna may have a positive antenna terminal coupled to the peripheral metal member and a ground terminal coupled to the ground. A return path for the first antenna may span the opening in parallel with the antenna feed. A plastic carrier may be mounted to a printed circuit and a metal housing structure using screws. The plastic carrier may support an antenna resonating element for the second antenna and may support the return path for the first antenna. The screws may short metal structures on the plastic carrier to the metal structures and traces on the printed circuit.