A charge pump circuit (300) includes a charge pump (330), and clocking circuitry that includes a clock generator (310) and a bypass circuit (320). The clocking circuitry generates clock signals and higher frequency alternative clock signals, for driving the charge pump. Upon start-up of the charge pump circuit and depending on a present value of an output voltage of the charge pump, the clocking circuitry couples to the charge pump either the alternative clock signals and not the clock signals, or the clock signals and not the alternative clock signals. Prior to completion of start-up of the charge pump circuit, at least two rows of pump unit cells are driven by a same alternative clock signal, thereby causing a pump unit cell in a row to charge/discharge at a same time as another pump unit cell in another row, thereby decreasing a start-up time of the charge pump circuit.