This paper presents an in-depth study of the theory and algorithms for the SPFD-based (Set of Pairs of Functions to be Distinguished) rewiring, and explores the flexibility in the SPFD computation. Our contributions are in the following two areas: (1) We present a theorem and a related algorithm for more precise characterization of feasible SPFD-based rewiring. Extensive experimental results show that for LUT-based FPGAs, the rewiring ability of our new algorithm is 70% higher than SPFDbased local rewiring algorithms (SPFD-LR)  and 18% higher than the recently developed SPFD-based global rewiring algorithm (SPFD-GR). (2) In order to achieve more rewiring ability on certain selected wires used in various optimizations, we study the impact of using different atomic SPFD pair assignment methods during the SPFD-based rewiring. We develop several heuristic atomic SPFD pair assignment methods for area or delay minimization and show that they lead to 10% more selected rewiring ability than the random (or arbitrary) assignment methods. When combining (1) and (2) together, we can achieve 38.1% higher general rewiring ability.