Current compilers lack precise timing models guiding their built-in optimizations. Hence, compilers apply ad-hoc heuristics during optimization to improve code quality. One of the most important optimizations is register allocation. Many compilers heuristically decide when and where to spill a register to memory, without having a clear understanding of the impact of such spill code on a program's run time. This paper extends a graph coloring register allocator such that it uses precise worst-case execution time (WCET) models. Using this WCET timing data, the compiler tries to avoid spill code generation along the critical path defining a program's WCET. To the best of our knowledge, this paper is the first one to present a WCET-aware register allocator. Our results underline the effectiveness of the proposed techniques. For a total of 46 realistic benchmarks, we reduced