An LED lamp with an integrated circuit, a rectifier, and a string of series-connected LEDs rectifies an incoming AC signal. The integrated circuit includes power switches that can separately and selectably short out a corresponding one of several groups of LEDs in an LED string across which the rectified AC signal is present. As the voltage across the string increases, the integrated circuit controls the power switches to increase the number of LEDs through which current flows, whereas as the voltage across the string decreases the integrated circuit controls the power switches to decrease the number of LEDs through which current flows. The flow of LED string current is broken to reduce flicker. Alternatively, a valley fill capacitor peaks LED current during the valleys of the incoming AC signal to reduce flicker. LED current is regulated to provide superior efficiency, reliability, power-factor correction, and lamp over-voltage, -current, and -temperature protection.