A new general method for building hybrid processors achieves higher performance in applications by allowing more powerful, tightly-coupled instruction set extensions to be implemented in reconfigurable logic. New instructions set configurations can be discovered and designed by automatic and semi-automatic methods. Improved reconfigurable execution units support deep pipelining, addition of additional registers and register files, compound instructions with many source and destination registers and wide data paths. New interface methods allow lower latency, higher bandwidth connections between hybrid processors and other logic.