This investigation examines the relationships between image fidelity, acceptability thresholds and scene content for images distorted by lossy compression. Scene characteristics of a sample set of images, with a wide range of representative scene content, were quantified, using simple measures (scene metrics), which had been previously found to correlate with global scene lightness, global contrast, busyness, and colorfulness. Images were compressed using the lossy JPEG 2000 algorithm to a range of compression ratios, progressively introducing distortion to levels beyond the threshold of detection. Twelve observers took part in a paired comparison experiment to evaluate the perceptibility threshold compression ratio. A further psychophysical experiment was conducted using the same scenes, compressed to higher compression ratios, to identify the level of compression at which the images became visually unacceptable. Perceptibility and acceptability thresholds were significantly correlated for the test image set; both thresholds also correlated with the busyness metric. Images were ranked for the two thresholds and were further grouped, based upon the relationships between perceptibility and acceptability. Scene content and the results from the scene descriptors were examined within the groups to determine the influence of specific common scene characteristics upon both thresholds.