Scientific programs often include multiple loops over the same data; interleaving parts of different loops may greatly improve performance. We exploit this in a compiler for Titanium, a dialect of Java. Our compiler combines reordering optimizations such as loop fusion and tiling with storage optimizations such as array contraction (eliminating or reducing the size of temporary arrays).The programmers we have in mind are willing to spend some time tuning their code and their compiler parameters. Given that, and the difficulty in statically selecting parameters such as tile sizes, it makes sense to provide automatic parameter searching alongside the compiler. Our strategy is to optimize aggressively but to expose the compiler's decisions to external control. We double or triple the performance of Gauss-Seidel relaxation and multigrid (versus an optimizing compiler without tiling and array contraction), and we argue that ours is the best compiler for that kind of program.