An LDO regulator includes two linear regulator circuits and an internal priority logic scheme that favors generating a regulated output voltage using a regulated supply voltage over an unregulated supply voltage. The unregulated supply voltage is applied to a first input terminal from a raw voltage source. The regulated supply voltage is applied to a second input terminal from, for example, a switching (e.g., BUCK) regulator. Two output devices are respectively connected between the first and second input terminals and the LDO output terminal. The first regulator circuit causes the first output device to supply the desired regulated output voltage while the switching regulator ramps up. Once the regulated supply voltage is high enough to allow regulation, the internal priority logic scheme disables the first regulator circuit, whereby the desired regulated output voltage is generated solely by the second regulator circuit through the second output device.