Accurately determining the attenuation along the propagation path leading to a region of interest could significantly improve diagnostic ultrasound tissue characterization since tissue characterization requires exact compensation for the frequency-dependent attenuation along the propagation path. In a previous study (JASA, 124:1367, 2008), it was shown that the total attenuation can be determined by using the backscattered echoes from multiple sources. The preliminary computer simulation results, had an average error between −0.3 and +0.2 dB/MHz for the cases tested with a trend towards increasing error with increasing correlation length (i.e., characteristic size of the tissue microstructure of the scattering medium) and attenuation along the propagation path. Therefore, the goal of this study was to improve the accuracy of previously derived algorithm and reduce the dependence of the algorithm on correlation length and attenuation. In this study, the previous derivations were redone and the assumptions made by the algorithm regarding the scattering properties of the medium and the shape of the backscattered power spectrum were relaxed. The revised algorithm was then verified using computer simulations of five sources (6, 8, 10, 12, and 14 MHz, 50% bandwidth) exposing a homogeneous tissue region. The simulated tissue had microstructure following a Gaussian spatial correlation function (i.e., exp (−0.827(kaeff)2) where k is the wavenumber) with effective radii, aeff, of 5–55 μm (one size per simulated case) placed at a density of 250/mm3 (∼5 scatterers/resolution cell for 14 MHz transducer). The attenuation of the tissue was also varied from 0.1 to 0.9 dB/cm-MHz. The computer simulations demonstrated that the modifications significantly improved the accuracy of the algorithm resulting in average errors between −0.04 and 0.1 dB/MHz which is three times better than the error performance of the original algorithm.