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The high correlation of the rain-free surface cross sections at two frequencies suggests that the estimate of differential path-integrated attenuation caused by precipitation along the radar beam can be obtained to a higher degree of accuracy than the path attenuation at either frequency. We explore this potential first analytically and then by examining data from the JPL dual-frequency airborne radar using measurements from the Tropical Composition, Cloud, and Climate Coupling experiment obtained during July-August 2007. Despite an improvement in the accuracy of the differential path attenuation, solving for parameters of the particle size distribution often requires not only this quantity but the single-wavelength path attenuation as well. We investigate a simple method of estimating the single-frequency path attenuation from the differential attenuation and compare this estimate with that derived directly from the surface return.