We analyze several representations for holographic data and determine the effectiveness of a common lossy compression algorithm for each representation. We demonstrate that a phase–amplitude representation, when used to represent holograms of diffuse objects, can be combined with a phase unwrapping algorithm to achieve much higher compression ratios (CRs) than direct compression of the complex valued holographic data. We compare the compression performance of the JPEG algorithm for several conventional and alternative holographic data representations. Additionally, we test two different phase unwrapping algorithms to improve phase compression performance. In particular, we propose and evaluate an alternative phase representation based on a quality guided phase unwrapping algorithm. This alternative representation offers higher performance to the other tested approaches, achieving CRs over 6 with a limited quality loss after reconstruction. We add the experimental reconstruction of the processed holograms to further validate our proposal.