A computer processor includes a branch prediction unit that includes a local branch predictor and a global branch predictor. Managing power consumption in such a computer processor includes, for each of a plurality of branch instructions: performing, by the local branch predictor, a local branch prediction; performing, by each of the global branch predictors, a global branch prediction; determining to utilize the local branch prediction over the global branch predictions as a branch prediction for the branch instruction; incrementing a value of a counter; determining whether the value of the counter exceeds a predetermined threshold; and if the value of the counter exceeds the predetermined threshold, powering down at least one of the global branch predictors and configuring the branch prediction unit to bypass the powered down global branch predictor for branch predictions of subsequent branch instructions.