We are developing a computerized system for automated segmentation of ureters on CTU, as a critical component for computer-aided diagnosis of ureter cancer. A challenge for ureter segmentation is the presence of regions not well opacified with intravenous (IV) contrast. We propose a COmbined Model-guided Path-finding Analysis and Segmentation System (COMPASS) to track the ureters in CTU. COMPASS consists of three stages: (1) adaptive thresholding and region growing, (2) edge profile extraction and feature analysis, and (3) path-finding and propagation. 114 ureters, filled with IV contrast material, on 74 CTU scans from 74 patients were segmented. On average the ureter occupied 286 CT slices (range:164 to 399, median:301). More than half of the ureters contained malignant or benign lesions and some had ureter wall thickening due to malignancy. A starting point for each of the 114 ureters was selected manually, which served as an input to the COMPASS, to initialize the tracking. The path-finding and segmentation are guided by anatomical knowledge of the ureters in CTU. The segmentation performance was quantitatively assessed by estimating the percentage of the length that was successfully tracked and segmented for each ureter. Of the 114 ureters, 75 (66%) were segmented completely (100%), 99 (87%) were segmented through at least 70% of its length, and 104 (91%) were segmented at least 50%. Previously, without the model-guided approach, 61 (54%) ureters were segmented completely (100%), 80 (70%) were segmented through at least 70% of its length, and 96 (84%) were segmented at least 50%. COMPASS improved the ureter tracking, including regions across ureter lesions, wall thickening and the narrowing of the lumen.