In order to statically schedule real-time tasks, predictions must be made for the worst-case execution time (WCET) of each task. Unfortunately, tightly predicting the WCET of a program is very challenging. I will present approaches for predicting the worst-case caching and pipeline behavior of a program, for dealing with dependencies on values that constrain the number of iterations for loops and the paths taken in a program, and for relating timing constraints in the source code to timing predictions on the machine code.