Electronic devices such as handheld devices may have wireless communications circuitry. The wireless communications circuitry may include a broadband antenna and circuitry that covers multiple communications bands. The broadband antenna may be formed from a parallel-fed dipole. The antenna may have first and second antenna resonating element regions on opposing sides of a slot. The slot may be an open slot that has one open end and one closed end. The slot may be formed from an opening in conductive housing structures in a conductive housing for an electronic device. The conductive housing structures may include sidewall structures, rear housing wall structures, and other conductive structures. The antenna may have a feed with a feed line that crosses the slot. An interposed dielectric substrate member may separate the feed line from the conductive structures. The feed line may have sections with different widths to minimize feed line length.