An optimized power saving technique is described for a processor, such as, for example, a graphic processing unit (GPU), which includes one or more processing cores and at least one data link interface. According to the technique, the processor is operable in a low power mode in which power to the at least one processing core is off and power to the at least one data link interface is on. This technique provides reduced exit latencies compared to currently available approaches in which the core power is turned off.