High-quality video is being increasingly delivered over Internet Protocol networks, which means that network operators and service providers need methods to measure the quality of experience (QoE) of the video services. In this paper, we propose a method to speed up the development of no-reference bitstream objective metrics for estimating QoE. This method uses full-reference objective metrics, which makes the process significantly faster and more convenient than using subjective tests. In this process, we have evaluated six publicly available full-reference objective metrics in three different databases, the EPFL-PoliMI database, the HDTV database, and the Live Video Wireless database, all containing transmission distortions in H.264 coded video. The objective metrics could be used to speed up the development process of no-reference real-time video QoE monitoring methods that are receiving great interest from the research community. We show statistically that the full-reference metric Video Quality Metric (VQM) performs best considering all the databases. In the EPFL-PoliMI database, SPATIAL MOVIE performed best and TEMPORAL MOVIE performed worst. When transmission distortions are evaluated, using the compressed video as the reference provides greater accuracy than using the uncompressed original video as the reference, at least for the studied metrics. Further, we use VQM to train a lightweight no-reference bitstream model, which uses the packet loss rate and the interval between instantaneous decoder refresh frames, both easily accessible in a video quality monitoring system.