Next-generation sequencing technologies are revolutionizing medicine. Data from sequencing technologies are typically represented as a string of bases, an associated sequence of per-base quality scores and other metadata, and in aggregate can require a large amount of space. The quality scores show how accurate the bases are with respect to the sequencing process, that is, how confident the sequencer is of having called them correctly, and are the largest component in datasets in which they are retained. Previous research has examined how to store sequences of bases effectively, here we add to that knowledge by examining methods for compressing quality scores. The quality values originate in a continuous domain, and so if a fidelity criterion is introduced, it is possible to introduce flexibility in the way these values are represented, allowing lossy compression over the quality score data.