Bacteriophage T4 gene 32 protein (gp32) is a well-studied representative of the large family of single-stranded DNA (ssDNA) binding proteins, which are essential for DNA replication, recombination and repair. Surprisingly, gp32 has not previously been observed to melt natural dsDNA. At the same time, *I, a truncated version of gp32 lacking its C-terminal domain (CTD), was shown to decrease the melting temperature of natural DNA by about 50 deg. C. This profound difference in the duplex destabilizing ability of gp32 and *I is especially puzzling given that the previously measured binding of both proteins to ssDNA was similar. Here, we resolve this apparent contradiction by studying the effect of gp32 and *I on the thermodynamics and kinetics of duplex DNA melting. We use a previously developed single molecule technique for measuring the non-cooperative association constants (K(ds)) to double-stranded DNA to determine K(ds) as a function of salt concentration for gp32 and *I. We then develop a new single molecule method for measuring K(ss), the association constant of these proteins to ssDNA. Comparing our measured binding constants to ssDNA for gp32 and *I we see that while they are very similar in high salt, they strongly diverge at [Na+] < 0.2 M. These results suggest that intact protein must undergo a conformational rearrangement involving the CTD that is in pre-equilibrium to its non-cooperative binding to both dsDNA and ssDNA. This lowers the effective concentration of protein available for binding, which in turn lowers the rate at which it can destabilize dsDNA. For the first time, we quantify the free energy of this CTD unfolding, and show it to be strongly salt dependent and associated with sodium counter-ion condensation on the CTD.