An electronic device may have a power system. The power system may receive power such as wireless power or wired power and may use a portion of the received power to charge a battery. Power consumption by control circuitry in the device can be adjusted by deactivating or activating processor cores in the control circuitry and by selectively starting or stopping software activities. By selectively reducing power consumption by circuitry in the electronic device other than battery charging circuitry in the power system that is charging the battery, additional power may be made available to charge the battery and/or battery capacity can be extended. The electronic device may reduce non-battery-charging activities in the device in response to information gathered with sensors such as motion and temperature information, information from the power system, information on device location, information on software settings, and other information.