In recent years, highly accurate branch predictors have been proposed primarily for high performance processors. Unfortunately such predictors are extremely energy consuming and in some cases not practical as they come with excessive prediction latency. Perceptron and O-GEHL are two examples of such predictors. To achieve high accuracy, these predictors rely on large tables and extensive computations and require high energy and long prediction delay. In this thesis we propose power optimization techniques that aim at reducing both computational complexity and storage size for these predictors. We show that by eliminating unnecessary data from computations, we can reduce both predictor's energy consumption and prediction latency. Moreover, we apply information theory findings to remove noneffective storage used by O-GEHL, without any significant accuracy penalty. We reduce the dynamic and static power dissipated in the computational parts of the predictors. Meantime we improve performance as we make faster prediction possible.