Interactive video segmentation systems aim at producing sub-pixel-level object boundaries for visual effect applications. Recent approaches mainly focus on using sparse user input (i.e. scribbles) for efficient segmentation; however, the quality of the final object boundaries is not satisfactory for the following reasons: (1) the boundary on each frame is often not accurate; (2) boundaries across adjacent frames wiggle around inconsistently, causing temporal flickering; and (3) there is a lack of direct user control for fine tuning. We propose Coherent Parametric Contours, a novel video segmentation propagation framework that addresses all the above issues. Our approach directly models the object boundary using a set of parametric curves, providing direct user controls for manual adjustment. A spatiotemporal optimization algorithm is employed to produce object boundaries that are spatially accurate and temporally stable. We show that existing evaluation datasets are limited and demonstrate a new set to cover the common cases in professional rotoscoping. A new metric for evaluating temporal consistency is proposed. Results show that our approach generates higher quality, more coherent segmentation results than previous methods.