Electronic devices such as portable electronic devices are provided. Power converters are provided that convert alternating-current power into direct-current power for powering the electronic devices. A power converter may rectify an alternating current line signal to produce a rectified alternating current signal having peaks and valleys. The power converter may have a capacitor and transformer coupled across the rectifier circuit. Power regulation switching circuitry in the power converter or the electronic device may regulate how much power is delivered to the electronic device. Relatively more power may be delivered during the peaks in the rectified signal than during the valleys. Pulsed power delivery may be controlled using control resources in the power converter, in the electronic device, or in both the power converter and electronic device.