This paper presents a new approach to resource-constrained compiler extraction of fine-grain parallelism, targeted towards VLIW supercomputers, and in particular, the IBM VLIW (Very Large Instruction Word) processor. The algorithms described integrate resource limitations into Percolation Scheduling—a global parallelization technique—to deal with resource constraints, without sacrificing the generality and completeness of Percolation Scheduling in the process. This is in sharp contrast with previous approaches which either applied only to conditional-free code, or drastically limited the parallelization process by imposing relatively local heuristic resource constraints early in the scheduling process.