Static compilers use profiling to predict run-time program behavior. Generally, this requires multiple input sets to capture wide variations in run-time behavior. This is expensive in terms of resources and compilation time. We introduce a new mechanism, 2D-profiling, which profiles with only one input set and predicts whether the result of the profile would change significantly across multiple input sets. We use 2D-profiling to predict whether a branch?s prediction accuracy varies across input sets. The key insight is that if the prediction accuracy of an individual branch varies significantly over a profiling run with one input set, then it is more likely that the prediction accuracy of that branch varies across input sets. We evaluate 2D-profiling with the SPEC CPU 2000 integer benchmarks and show that it can identify input-dependent branches accurately.