With the advent of modern computing and imaging technologies, the use of digital holography became practical in many applications such as microscopy, interferometry, non-destructive testing, data encoding, and certification. In this respect the need for an efficient representation technology becomes imminent. However, microscopic holographic off-axis recordings have characteristics that differ significantly from that of regular natural imagery, because they represent a recorded interference pattern that mainly manifests itself in the high-frequency bands. Since regular image compression schemes are typically based on a Laplace frequency distribution, they are unable to optimally represent such holographic data. However, unlike most image codecs, the JPEG 2000 standard can be modified to efficiently cope with images containing such alternative frequency distributions by applying the arbitrary wavelet decomposition of Part 2. As such, employing packet decompositions already significantly improves the compression performance for off-axis holographic images over that of regular image compression schemes. Moreover, extending JPEG 2000 with directional wavelet transforms shows even higher compression efficiency improvements. Such an extension to the standard would only require signaling the applied directions, and would not impact any other existing functionality. In this paper, we show that wavelet packet decomposition combined with directional wavelet transforms provides efficient lossy-to-lossless compression of microscopic off-axis holographic imagery.