Electronic devices may be provided that contain wireless communications circuitry. The wireless communications circuitry may include radio-frequency transceiver circuitry coupled to an adjustable antenna. The adjustable antenna may contain conductive antenna structure such as conductive electronic device housing structures. Electrical components such as switches and resonant circuits may be used in configuring the antenna to operate in two or more different antenna modes at different respective communications bands. Control circuitry may be used in controlling the switches. The antenna may be configured to operate as an inverted-F antenna in one mode of operation and a slot antenna in a second mode of operation.