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Micro-computed tomography (micro-CT) is an important tool in biomedical research and preclinical applications that can provide visual inspection of and quantitative information about imaged small animals and biological samples such as vasculature specimens. Currently, micro-CT imaging uses projection data acquired at a large number (300-1000) of views, which can limit system throughput and potentially degrade image quality due to radiation-induced deformation or damage to the small animal or specimen. In this work, we have investigated low-dose micro-CT and its application to specimen imaging from substantially reduced projection data by using a recently developed algorithm, referred to as the adaptive-steepest-descent-projection-onto-convex-sets (ASD-POCS) algorithm, which reconstructs an image through minimizing the image total-variation and enforcing data constraints. To validate and evaluate the performance of the ASD-POCS algorithm, we carried out quantitative evaluation studies in a number of tasks of practical interest in imaging of specimens of real animal organs. The results show that the ASD-POCS algorithm can yield images with quality comparable to that obtained with existing algorithms, while using one-sixth to one quarter of the 361-view data currently used in typical micro-CT specimen imaging.