DNA strand displacement systems have transformative potential in synthetic biology. While powerful examples have been reported in DNA nanotechnology, such systems are plagued by leakage, which limits network stability, sensitivity, and scalability. An approach to mitigate leakage in DNA nanotechnology, which is applicable to synthetic biology, is to introduce mismatches to complementary fuel sequences at key locations. However, this method overlooks nuances in the secondary structure of the fuel and substrate that impact the leakage reaction kinetics in strand displacement systems. In an effort to quantify the impact of secondary structure on leakage, we introduce the concepts of availability and mutual availability and demonstrate their utility for network analysis. Our approach exposes vulnerable locations on the substrate and quantifies the secondary structure of fuel strands. Using these concepts, a 4-fold reduction in leakage has been achieved. The result is a rational design process that efficiently suppresses leakage and provides new insight into dynamic nucleic acid networks.