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The problem of "debloating" programs for security and performance purposes has begun to see increased attention. Of particular interest in many environments is debloating commodity off-the-shelf (COTS) software, which is most commonly made available to end users as stripped binaries (i.e., neither source code nor symbol-table/debugging information is available). Toward this end, we created a system, called GenXGen[MC], that specializes stripped binaries. Many aspects of the debloating problem can be addressed via techniques from the literature on partial evaluation. However, applying such techniques to real-world programs, particularly stripped binaries, involves non-trivial state-management manipulations that have never been addressed in a completely satisfactory manner in previous systems. In particular, a partial evaluator needs to be able to (i) save and restore arbitrary program states, and (ii) determine whether a program state is equal to one that arose earlier. Moreover, to specialize stripped binaries, the system must also be able to handle program states consisting of memory that is undifferentiated beyond the standard coarse division into regions for the stack, the heap, and global data. This paper presents a new approach to state management in a program specializer. The technique has been incorporated into GenXGen[MC], a novel tool for producing machine-code generating extensions. Our experiments show that our solution to issue (i) significantly decreases the space required to represent program states, and our solution to issue (ii) drastically improves the time for producing a specialized program (as much as 13,000x speedup).