Micro-CT enables convenient visualization and quantitative analysis of small animals and biological tissue samples. However, high-quality volume images in general require acquisition of cone-beam projection data from hundreds of view angles. This prolonged imaging process limits system throughput and may cause potential radiation damage to the imaged objects. It is therefore desirable to have a technique which can generate volume images with satisfactory quality, but from a smaller amount of projection data. On the other hand, many objects subject to the micro-CT scans have sparse spatial distribution, and this sparcity could be exploited and incorporated as prior knowledge in innovative design of algorithms that are capable of reconstructing images from few-view projection data. In this work we applied a new iterative algorithm based upon constrained total-variation minimization to reconstructing images from as few as five projections. Preliminary results suggest that the algorithm can yield potentially useful images from substantially less projection data than required by existing algorithms. This has practical implications of reducing scanning time and minimizing radiation damage to the imaged objects.