The described embodiments include an apparatus that controls voltages for an integrated circuit chip having a set of circuits. The apparatus includes a switching voltage regulator separate from the integrated circuit chip and two or more low dropout (LDO) regulators fabricated on the integrated circuit chip. The switching voltage regulator provides an output voltage that is received as an input voltage by each of the two or more LDO regulators, and each of the two or more LDO regulators provides a local output voltage, each local output voltage received as a local input voltage by a different subset of the circuits in the set of circuits. During operation, a controller sets an operating point for each of the subsets of circuits based on a combined power efficiency for the subsets of the circuits and the LDO regulators, each operating point including a corresponding frequency and voltage.