A power converter circuit may convert alternating current signals into direct current signals. A load may be powered from output terminals that are provided with the direct current signals. The power converter circuit may have a transformer with primary and secondary sides. A transistor on the primary side may be controlled using a pulse width modulation controller. A diode may be coupled in series with the secondary side of the transformer and the load. To improve efficiency at larger load currents, a synchronous rectifier control circuit may modulate a transistor on the secondary side that is coupled in parallel with the diode. The synchronous rectifier control circuit may monitor voltage pulses on the transistor on the secondary side or may make direct load current measurements to ascertain how much load current is flowing. Under low or no load conditions, synchronous rectification can be inhibited to improve efficiency.