Measurements of lung nodule volume with multi-detector computed tomography (MDCT) have been shown to be more accurate and precise compared to conventional lower dimensional measurements. Quantifying the size of lesions is potentially more difficult when the object-to-background contrast is low as with lesions in the liver. Physical phantom and simulation studies are often utilized to analyze the bias and variance of lesion size estimates because a ground truth or reference standard can be established. In addition, it may also be useful to derive theoretical bounds as another way of characterizing lesion sizing methods. The goal of this work was to study the performance of a MDCT system for a lesion volume estimation task with object-to-background contrast less than 50 HU, and to understand the relation among performances obtained from phantom study, simulation and theoretical analysis. We performed both phantom and simulation studies, and analyzed the bias and variance of volume measurements estimated by a matched-filter-based estimator. We further corroborated results with a theoretical analysis to estimate the achievable performance bound, which was the Cramer-Rao's lower bound (CRLB) of minimum variance for the size estimates. Results showed that estimates of non-attached solid small lesion volumes with object-to-background contrast of 31-46 HU can be accurate and precise, with less than 10.8% in percent bias and 4.8% in standard deviation of percent error (SPE), in standard dose scans. These results are consistent with theoretical (CRLB), computational (simulation) and empirical phantom bounds. The difference between the bounds is rather small (for SPE less than 1.9%) indicating that the theoretical- and simulation-based performance bounds can be good surrogates for physical phantom studies.