Extensible processors allow addition of application-specific custom instructions to the core instruction set architecture. However, it is computationally expensive to automatically select the optimal set of custom instructions. Therefore, heuristic techniques are often employed to quickly search the design space. In this paper, we present an efficient algorithm for exact enumeration of all possible candidate instructions given the dataflow graph (DFG) corresponding to a code fragment. Even though this is similar to the "subgraph enumeration" problem (which is exponential), we find that most subgraphs are not feasible candidates for various reasons. In fact, the number of candidates is quite small compared to the size of the DFG. Compared to previous approaches, our technique achieves orders of magnitude speedup in enumerating these candidate custom instructions for very large DFGs.