Predicting the worst-case execution time (WCET) 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 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 value-dependent 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 value-dependent constraints by a compiler and automatically exploiting these constraints within a timing analyzer. The result is tighter timing analysis predictions without requiring additional interaction with a user.