We describe a new method to recover the distribution of distances between two sites on flexible molecules, which requires only steady state measurements of fluorescence intensities. We used collisional quenching of the donor fluorescence to vary the characteristic Förster distance (R0) for energy transfer. The measured transfer efficiencies for each value of R0 provide different samples of the distance distribution. The R0-dependent transfer efficiencies, when analyzed by non-linear least squares, were found to reliably determine the distance distribution, as shown by evaluation of the uncertainties in the distribution and by agreement with the frequency-domain method (Chem. Phys. Letters 138 (1987) 587).