When using the backscatter coefficient (BSC) to estimate quantitative ultrasound parameters such as the effective scatterer diameter (ESD) and the effective acoustic concentration (EAC), it is necessary to assume that the interrogated medium contains diffuse scatterers. Structures that invalidate this assumption can affect the estimated BSC parameters in terms of increased bias and variance and decrease performance when classifying disease. In this work, a method was developed to mitigate the effects of echoes from structures that invalidate the assumption of diffuse scattering, while preserving as much signal as possible for obtaining diffuse scatterer property estimates. Backscattered signal sections that contained nondiffuse signals were identified and a windowing technique was used to provide BSC estimates for diffuse echoes only. Experiments from physical phantoms were used to evaluate the effectiveness of the proposed BSC estimation methods. Tradeoffs associated with effective mitigation of specular scatterers and bias and variance introduced into the estimates were quantified. Analysis of the results suggested that discrete prolate spheroidal (PR) tapers with gaps provided the best performance for minimizing BSC error. Specifically, the mean square error for BSC between measured and theoretical had an average value of approximately 1.0 and 0.2 when using a Hanning taper and PR taper respectively, with six gaps. The BSC error due to amplitude bias was smallest for PR (Nω = 1) tapers. The BSC error due to shape bias was smallest for PR (Nω = 4) tapers. These results suggest using different taper types for estimating ESD versus EAC.