In this paper, we report the results of a set of psychophysical experiments that measure the perceptual strengths of videos with different combinations of blockiness, blurriness, and packet-loss artifacts and the overall annoyance. Participants were instructed to search each video for impairments and rate the strength of their individual features (artifacts). A repeated measure Anova (RM-ANOVA) performed on the data showed that artifact physical strengths have a significant effect on annoyance judgments. We tested and reported a set of linear models on the experimental data and we found that all these models give a good description of the relation between individual artifact perceptual strengths and the overall annoyance. In other words, all models presented a very good correlation with the experimental data, showing that annoyance can be modeled as a multidimensional function of the individual artifact perceptual strengths. Additionally, results show that there are interactions among artifact signals.