A delay circuit provides a substantially constant delay over a range of power-supply voltages. The delay circuit includes an input terminal that receives an input signal, an output terminal that provides an output signal, and a supply terminal that receives a supply voltage. A delay stage is coupled between the input and the output terminals and, when the supply voltage has a predetermined value, generates the output signal a predetermined delay time after it receives the input signal. A control stage is coupled between the supply terminal and the delay stage and regulates the supply current that flows between the supply terminal and the delay stage such that the delay time of the delay stage remains substantially equal to the predetermined delay time as the supply voltage varies from the predetermined value.