In one embodiment, a processor includes at least one sleep block and a central sleep controller. The at least one sleep block may include at least one execution unit, at least one processor component, and sleep logic. The central sleep controller may be to program the sleep logic to perform at least one sleep transition for the at least one sleep block, and to operate in a first sleep mode. The sleep logic may be to perform the at least one sleep transition for the at least one sleep block without waking the central sleep controller from the first sleep mode. Other embodiments are described and claimed.