Wireless circuitry in an electronic device may contain output power amplifier circuitry for amplifying transmitted radio-frequency signals. The power amplifier circuitry may be powered using a bias voltage. The magnitude of the bias voltage can be selectively reduced to conserve power. Control circuitry can maintain a table of bias voltage settings to use under various conditions. These conditions may include required output powers as determined by link quality, transmission mode status, and required data rates. When link quality is low or when high data rates are required, the bias voltage can be maintained at a relatively high level to ensure that the power amplifier operates linearly and does not exhibit excessive noise. When link quality is high or when data rates are low as with voice calls, the bias voltage can be reduced to conserve power.