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Efficiency and flexibility are critical, but often conflicting, design goals in embedded system design. The recent emergence of extensible processors promises a favorable tradeoff between efficiency and flexibility, while keeping design turnaround times short. Current extensible processor design flows automate several tedious tasks, but typically require designers to manually select the parts of the program that are to be implemented as custom instructions. In this work, we describe an automatic methodology to select custom instructions to augment an extensible processor, in order to maximize its efficiency for a given application program. We demonstrate that the number of custom instruction candidates grows rapidly with program size, leading to a large design space, and that the quality (speedup) of custom instructions varies significantly across this space, motivating the need for the proposed flow. Our methodology features cost functions to guide the custom instruction selection process, as well as static and dynamic pruning techniques to eliminate inferior parts of the design space from consideration. Further, we employ a two-stage process, wherein a limited number of promising instruction candidates are first selected, and then evaluated in more detail through cycle-accurate instruction set simulation and synthesis of the corresponding hardware, to identify the custom instruction combinations that result in the highest program speedup or maximize speedup under a given area constraint. We have evaluated the proposed techniques using a state-of-the-art extensible processor platform, in the context of a commercial design flow.