Handheld electronic devices are provided that contain wireless communications circuitry. The wireless communications circuitry may include antenna structures. An antenna may be located in an upper right corner of the handheld device as the handheld device is operated in a portrait mode. When the handheld device is rotated counterclockwise and operated in a landscape mode, the antenna is located in an unobstructed upper left corner of the device. The antenna may be formed from a strip of conductor. A proximal end of the strip of conductor may be connected to a transmission line. A distal end of the strip of conductor may be routed away from housing surfaces by bends formed in the strip. A printed circuit board in the handheld electronic device may have a hole. The distal end of the strip of conductor may be located adjacent to the hole.