We propose a novel approach to automatically tracking elliptical cell populations in time-lapse image sequences. Given an initial segmentation, we account for partial occlusions and overlaps by generating an over-complete set of competing detection hypotheses. To this end, we fit ellipses to portions of the initial regions and build a hierarchy of ellipses, which are then treated as cell candidates. We then select temporally consistent ones by solving to optimality an integer program with only one type of flow variables. This eliminates the need for heuristics to handle missed detections due to partial occlusions and complex morphology. We demonstrate the effectiveness of our approach on a range of challenging sequences consisting of clumped cells and show that it outperforms state-of-the-art techniques.