Need help with tryptophan fluorescence assay

I'm trying to determine Kd values for protein:RNA binding using tryptophan fluorescence.

Buffer:

10mM HEPES (pH 7.5)

100mM NaCL

4mM MgCl2

1mM TCEP

[protein] = 0.25uM; RNA is titrated in 0 - 4uM.

Instruments used:

-Perkin Elmer LS 55

-Varian Cary Eclipse

Fluoresence quenching data is corrected for the inner filter effect ad fit to a quadratic equation.

Problem:

Im measuring Kd's in the nM range for my protein:RNA complex, but when I titrate RNA into BSA or lysozyme as negative controls, I also measure nM Kds. Same goes for my protein:poly-dIdC.

This is very confusing. Why would I be measuring such tight binding amongst molecules that should have no specific binding?

I've increased [NaCl] to 250 nM (to reduce non-specific binding), conducted the experiment in 25% glycerol (to reduce collisional quenching), neither have alleviated the issue.

Can anyone provide rationale for my results and suggest experiment to separate the specific vs. non-specific interactions that may be leading to my results?

thanks.