Electronic devices may be provided that contain conductive paths. A conductive path may be formed from an elongated metal member that extends across a dielectric gap in an antenna. The antenna may be formed from conductive structures that form an antenna ground and conductive structures that are part of a peripheral conductive housing member in the electronic device. The gap may separate the peripheral conductive housing member from the conductive structures. A conductive path may also be formed using one or more springs. A spring may be welded to a conductive member and may have prongs that press against an additional conductive member when the spring is compressed. The prongs may have narrowed tips, curved shapes, and burrs that help form a satisfactory electrical contact between the spring prongs and the additional conductive member.