A method is provided for multiplexing video services with data services in a constrained delivery pipeline. A soft upper bound for the video data bandwidth for a current schedule window BWvideosoft(i) is generated, wherein the soft upper bound for the video data bandwidth such that an average video data bandwidth over a time period T is no greater than a hard upper bound for the video data bandwidth BVvideo. The video data is then multiplexed with the other data according to the soft upper bound for the video data bandwidth BWvideosoft(i).