Quantifying the size of the tissue microstructure using the backscattered power spectrum has had limited success due to frequency-dependent attenuation along the propagation path, thus masking the frequency dependence of the scatterer size. Previously, the SPECTRAL FIT algorithm was developed to solve for total attenuation and scatterer size simultaneously [Bigelow et al., J. Acoust. Soc. Am. 117, 1431-1439 (2005)]. Herein, the outcomes from signal processing strategies on the SPECTRAL FIT algorithm are investigated. The signal processing methods can be grouped into two categories, viz., methods that improve the performance of the algorithm and methods that provide insight. The methods that improve the performance include compensating for the windowing function used to gate the time-domain signal, averaging the spectra in the normal frequency domain rather than the log domain to improve the precision of the scatterer size and attenuation estimates, improving the selection of the usable frequency range for the SPECTRAL FIT algorithm, and improving the compensation for electronic noise. The methods that provide insight demonstrate that the anomalous rapid fluctuations of the backscattered power spectrum do not affect the SPECTRAL FIT algorithm, and accurate attenuation estimates can be obtained even when the correct scatterer geometry (i.e., form factor) is not known.