As the issue rate and depth of pipelining of high performance Superscalar processors increase, the importance of an excellent branch predictor becomes more vital to delivering the potential performance of a wide-issue, deep pipelined microarchitecture. We propose a new dynamic branch predictor (Two-Level Adaptive Branch Prediction) that achieves substantially higher accuracy than any other scheme reported in the literature. The mechanism uses two levels of branch history information to make predictions, the history of the last k branches encountered, and the branch behavior for the last s occurrences of the specific pattern of these k branches. We have identified three variations of the Two-Level Adaptive Branch Prediction, depending on how finely we resolve the history information gathered. We compute the hardware costs of implementing each of the three variations, and use these costs in evaluating their relative effectiveness. We measure the branch prediction accuracy of the three variations of two-Level Adaptive Branch Prediction, along with several other popular proposed dynamic and static prediction schemes, on the SPEC benchmarks. We show that the average prediction accuracy for Two-Level Adaptive Branch Prediction is 97 percent, while the other known schemes achieve at most 94.4 percent average prediction accuracy. We measure the effectiveness of different prediction algorithms and different amounts of history and pattern information. We measure the costs of each variation to obtain the same prediction accuracy.