The disclosed embodiments provide a system that facilitates power management in a multi-core processor. During operation, the system detects a change related to a number of active processor cores in the multi-core processor. (Within this system, a given processor core can reside in an active state, wherein the given processor core can draw an active power, or alternatively in a constrained state, wherein the given processor core can draw a constrained power, which is less than the active power.) In response to detecting the change, the system computes a new current limit ICCMAX for the multi-core processor based on the number of active and constrained processor cores. Finally, the system communicates ICCMAX to a power-management mechanism within the multi-core processor. This enables the power-management mechanism to use ICCMAX to account for power saved by the constrained processor cores when the multi-core system is subsequently determining whether to change its operating frequency.