A branch prediction unit includes a local branch prediction and a global branch prediction. A global branch prediction utilizes a global history shift register to record the behavior of conditional branches. In some cases, a conditional branch may behave in a static manner, either always being taken or not taken, while resident in an instruction cache. Such static behaving conditional branches do not need a global history for prediction and contend with other conditional branches for global branch history training. By utilizing a dynamic branch classification scheme, branches requiring global history prediction can be identified and static behaving conditional branches may be prevented from polluting the global history. All conditional branches are initially classified as local and do not participate in global history training. Only after two mispredictions are branches recognized as exhibiting dynamic behavior and classified as global. These branches classified as global may then participate in global history training and utilize a global history based branch prediction.