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In this paper, we introduce and analyze the Optimized GEometric History Length (O-GEHL) branch Predictor that efficiently exploits very long global histories in the100-200 bits range. The GEHL predictor features several predictor tables T(i) (e.g. 8) indexed through independent functions of the global branch history and branch address. The set of used global history lengths forms a geometric series, i.e., L(j) = \alpha ^{i - 1} L(1).This allows the GEHL predictor to efficiently capture correlation on recent branch outcomes as well as on very old branches. As on perceptron predictors, the prediction is computed through the addition of the predictions read on the predictor tables. The O-GEHL predictor further improves the ability of the GEHL predictor to exploit very long histories through the addition of dynamic history fitting and dynamic threshold fitting. The O-GEHL predictor can be ahead pipelined to provide in time predictions on every cycle.