Pulse-echo ultrasound display relies on many assumptions that are known to be incorrect. Departure from these makes interpretation of conventional ultrasound images difficult, and three-dimensional (3-D) visualizations harder still. For instance, shadowing and enhancement are the result of an incorrect assumption that sound attenuation is a function only of depth. Attempts to reduce such artefacts by estimating attenuation locally have been frustrated by large statistical variations and the influence of scatterer type. We address the latter by examining the influence of scatterer type on two existing attenuation estimation algorithms. This analysis is novel for one of the algorithms, and contains a correction to previously published work for the other. We then propose a novel algorithm that is less sensitive to scatterer variation. We also present a novel technique for handling large statistical variations based on combined assumptions of monotonicity and smoothness. We then assess the performance of each algorithm for correcting shadowing and enhancement in in vitro data, using a real time 3-D radio frequency (RF) ultrasound acquisition system developed for this purpose. The results show visible differences in attenuation estimates from each technique, which are supported by the theoretical analysis. The novel attenuation estimation algorithm does show less sensitivity to scatterer variation, though it results in a more noisy estimate. Nevertheless, the novel technique for reducing statistical variations is sufficient to allow some degree of correction of shadowing and enhancement in each case.