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Designers have invested much effort in developing accurate branch predictors with short learning periods. Such techniques rely on exploiting complex and relatively large structures. Although exploiting such structures is necessary to achieve high accuracy and fast learning, once the short learning phase is over, a simple structure can efficiently predict the branch outcome for the majority of branches. Moreover, for a large number of branches, once the branch reaches the steady state phase, updating the branch predictor unit is unnecessary since there is already enough information available to the predictor to predict the branch outcome accurately. Therefore, aggressive usage of complex large branch predictors appears to be inefficient since it results in unnecessary energy consumption. In this work we introduce Selective Predictor Access (SEPAS) to exploit this design inefficiency. SEPAS uses a simple power efficient structure to identify well behaved branch instructions that are in their steady state phase. Once such branches are identified, the predictor is no longer accessed to predict their outcome or to update the associated data. We show that it is possible to reduce the number of predictor accesses and energy consumption considerably with a negligible performance loss (worst case 0.25%).