Circuits naturally exhibit recurring patterns of local interconnect. Hardening those patterns when designing Field Programmable Gate Array (FPGA) clusters can both eliminate slow programmable connections from the critical path and remove the need for transistors to implement them. While we may be able to manually design such clusters, based on intuition and observations, such an endeavour will always leave us in doubt whether we have used the potential of cheap and fast hardened connections to the fullest. On the other hand, since there are similar to 10(7) possible patterns of interconnect among only eight 5-input Look-Up Tables (LUTs), even without considering the possibilities for enforcing input sharing, performing an exhaustive exploration of the design space seems like a task as daunting as finding a needle in a haystack. Despite their enormous sizes, design spaces spanned by such cluster architectures are very well structured. In this paper, we leverage that structure to limit the search to only those points of the space that may perform better than any chosen reference. We demonstrate the usefulness of our techniques by narrowing the space spanned by five 5-LUT structures from hundreds of millions to a set of 261 structures that achieve >= 80% utilization on a set of standard benchmarks, while requiring only 12 external inputs. We believe that the exploration techniques presented here are an important step towards truly exploiting the potentials of hardening programmable connections.