Automatic generation of Instruction Set Extensions (ISEs), executed on a custom processing unit or a coprocessor, is an important step towards processor customization. A typical goal of a manual designer is to combine a large number of atomic instructions into an ISE satisfying microarchitectural constraints. However, memory operations pose a challenge for previous ISE approaches by limiting the size of the resulting instruction. In this report, we introduce memory elements into custom units which result in ISEs closer to those sought after by the designers. We consider two kinds of memory elements for mapping to the specialized hardware: small hardware tables and architecturally-visible state registers. We devised a genetic algorithm to specifically exploit opportunities of introducing memory elements during ISE generation. Finally, we demonstrate the effectiveness of our approach by a detailed study of the variation in performance, area and energy in the presence of the generated ISEs, on a number of MediaBench, EEMBC and cryptographic applications. With the introduction of memory, the average speedup varied from 2.7X to 5X depending on the architectural configuration with a nominal area overhead. Moreover, we obtained an average energy reduction of 26% with respect to a 32-KB cache.