An accessory such as a wireless headset may have an antenna for transmitting and receiving wireless signals. First and second earbuds may be coupled to different ends of a housing for the accessory. A rigid flex printed circuit board in the housing may include a rigid printed circuit portion. The rigid printed circuit portion may include first and second rigid printed circuit layers. A first portion of a flexible printed circuit may be interposed between the first and second rigid layers. A second portion of the flexible printed circuit may extend from an end of the rigid layers and may be wrapped around the first rigid layer. Planar inverted-F antenna resonating element, antenna shorting, and antenna feeding traces may be formed on the second portion of the flexible printed circuit. The efficiency of the antenna may be undisturbed by the presence of a user's body adjacent to the accessory.