Compression is increasingly used in medical applications to enable efficient and universally accessible electronic health records. However, lossy compression introduces artifacts that can alter diagnostic accuracy, interfere with image processing algorithms and cause liability issues in cases of diagnostic errors. Compression guidelines were introduced to mitigate these issues and foster the use of modern compression algorithms with diagnostic imaging. However, these guidelines are usually defined as maximum compression ratios for each imaging protocol and do not take compressibility variations due to image content into account. In this paper we have evaluated the compressibility of thousands of computed tomography slices of an anthropomorphic thoracic phantom acquired with different parameters. We have shown that exposure, slice thickness and reconstruction filters have a significant impact on compressibility suggesting that guidelines based solely on compression ratios may be inadequate.