In this paper we present the results of a psychophysical experiment which measured the overall annoyance and artifact strengths of videos with different combinations of blocky, blurry, noisy, and ringing synthetic artifacts inserted in limited spatio-temporal regions. The test subjects were divided into two groups, which performed different tasks - 'Annoyance Judgment' and 'Strength Judgment'. The 'Annoyance' group was instructed to search each video for impairments and make an overall judgment of their annoyance. The 'Strength' group was instructed to search each video for impairments, analyze the impairments into individual features (artifacts), and rate the strength of each artifact using a scale bar. An ANOVA of the overall annoyance judgments showed that the artifact physical strengths had a significant effect on the mean annoyance value. It also showed interactions between the video content (original) and 'noisiness strength', 'original' and 'blurriness strength', 'blockiness strength' and 'noisiness strength', and 'blurriness strength' and 'noisiness strength'. In spite of these interactions, a weighted Minkowski metric was found to provide a reasonably good description of the relation between individual defect strengths and overall annoyance. The optimal value found for the Minkowski exponent was 1.03 and the best coefficients were 5.48 (blockiness), 5.07 (blurriness), 6.08 (noisiness), and 0.84 (ringing). We also fitted a linear model to the data and found coefficients equal to 5.10, 4.75, 5.67, and 0.68, respectively.