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Predicting the worst-case execution time (WCET) and best-case execution time (BCET) of a real-time program is a challenging task. Though much progress has been made in obtaining tighter timing predictions by using techniques that model the architectural features of a machine, significant overestimations of WCET and underestimations of GCET can still occur. Even with perfect architectural modeling, dependencies on data values can constrain the outcome of conditional branches and the corresponding set of paths that can be taken in a program. While branch constraint information has been used in the past by some timing analyzers, it has typically been specified manually, which is both tedious and error prone. This paper describes efficient techniques for automatically detecting branch constraints by a compiler and automatically exploiting these constraints within a timing analyzer. The result is significantly tighter timing analysis predictions without requiring additional interaction with a user.