Methods and apparatuses relating to dynamic asymmetric scaling of branch predictor tables are described. Branch predictor circuits to perform dynamic asymmetric scaling of branch predictor tables are also described. In one embodiment, a processor includes an execution unit to execute a branch instruction; and a branch predictor to generate a prediction for the branch instruction from either of a plurality of global history prediction tables of differing history lengths and a floating global history prediction table, wherein the branch predictor is to: for each of the plurality of global history prediction tables, track a total number of unique entries that provide a correct prediction which is not available in a global history prediction table of lower history length within a monitoring period that includes execution of a plurality of instances of the branch instruction, and assign the floating global history prediction table as an extension to a global history prediction table of the plurality of global history prediction tables having a greatest total number of unique useful entries in the monitoring period.