Tree-like vessel structures are an information-rich source for many image analysis tasks. Hence tracking algorithms extracting such structures have wide applicability. However, due to image artifacts and the minute nature of vessels, these algorithms face several challenges; two of the most common ones are 1) early termination, where tracking stops before the structure ends and 2) leaking, where tracking leaks into nearby closed organs or irrelevant structures. To address these issues, this paper makes two main contributions: a generic rebooting scheme that identifies early terminations and then restarts tracking to track objects in their entirety and a modelbased pruning algorithm that uses global optimization to identify and mitigate leaking. The performance of the proposed algorithm is demonstrated by tracking coronary arteries on 3D cardiac Computed Tomography Angiography (CTA) data from 28 human subjects. Our methods dramatically improve tracking results by detecting and recovering from early terminations and identifying and removing leaking in 98% (63 of 64) branches, with a single erroneously removed valid branch.