Electronic devices and accessories are provided that may communicate over wired communications paths. The electronic devices may be portable electronic devices such as cellular telephones or media players and may have audio connectors such as 3.5 mm audio jacks. The accessories may be headsets or other equipment having mating 3.5 mm audio plugs and speakers for playing audio. Microphones may be included in an accessory to gather voice signals and noise cancellation signals. Analog-to-digital converter circuitry in the accessory may digitize the microphone signals. Digital voice signals and voice noise cancellation signals can be transmitted over the communications path and processed by audio digital signal processor circuitry in an electronic device. Digital-to-analog converter circuitry in the accessory may convert digital audio signals to analog speaker signals. Digital noise cancellation signals may use digital noise signals to cancel noise from digital audio signals that have been received from an electronic device.