In one embodiment, the present invention includes a processor having a first domain with a first compute engine and a second domain with a second compute engine, where each of these domains can operate at an independent voltage and frequency. A first logic may be present to update a power bias value used to control dynamic allocation of power between the first and second domains based at least in part on a busyness of the second domain. In turn, a second logic may dynamically allocate at least a portion of a power budget for the processor between the domains based at least in part on this power bias value. Other embodiments are described and claimed.