An electronic device such as a cellular telephone or other device may have a housing with front and rear faces joined by a sidewall. A display may be mounted on the front face. The electronic device may include multiple ambient light sensors such as a front ambient light sensor on the front face and one or more supplemental ambient light sensors on the rear face and/or on the sidewall. The front ambient light sensor gathers a front ambient light intensity measurement and the supplemental ambient light sensor gathers a supplemental ambient light intensity measurement. During operation, control circuitry in the electronic device adjusts the display brightness based on data from the ambient light sensors. The control circuitry may implement power saving restrictions that limit when the supplemental ambient light intensity measurement is taken into account and/or that impose a brightness cap on the display brightness.