In multi-pinhole SPECT, overlapping the projections from different pinholes has been used to increase sensitivity. However, the prevailing view is that the overall quality of the reconstructed image is not improved by the overlaps in the projections. It is often stated in literatures that overlaps introduce ambiguous information, which can lead to nonuniqueness of solution for the inverse problem, and thus artifacts are introduced in the reconstructed image. On the other hand, contrary to the prevailing view, a recent study on slit-slat collimators shows that artifacts can be removed with the “help” of an extra complete nonoverlapped projection data set. In this paper, two types of artifact-free projection overlaps are defined in general, and the criteria for designing artifact-free multi-pinhole systems with overlaps are proposed. It is shown that once the criteria are satisfied, the solution of the inverse problem is unique, and thus no artifact is expected in the reconstructed image. Via extensive simulation study, various artifact-free overlapping multi-pinhole systems are designed and validated. It is shown that overlaps in the artifact-free systems can improve contrast-to-noise ratio (CNR). With a proper design, the CNR for an artifact-free overlapping system can be significantly higher than that for the corresponding nonoverlapping system. The improved image quality is also confirmed with noisy reconstructions.