An electronic device may contain wireless circuitry that transmits and receives radio-frequency signals through antenna structures. Power amplifier circuitry may amplify the radio-frequency signals that are being transmitted. An adjustable voltage supply may supply an adjustable power amplifier bias voltage to the power amplifier circuitry. The power amplifier circuitry may include multiple power amplifiers each of which may handle signals transmitted using a different cellular telephone standard. For each cellular telephone standard, multiple modulation schemes may be supported. Some modulation schemes may have greater power amplifier linearity requirements than others. Control circuitry can adjust the adjustable power amplifier bias voltage in real time to select an optimum power amplifier bias voltage based on the current cellular telephone standard, modulation scheme, power amplifier gain state, and operating frequency in use.