We present the results of applying data compression techniques to encrypted three-dimensional objects. The objects are captured using phase-shift digital holography and encrypted using a random phase mask in the Fresnel domain. Lossy quantisation is combined with lossless coding techniques to quantify compression rates. Lossless compression alone applied to the encrypted holographic data achieves compression rates lower than 1.05. When combined with quantisation and an integer encoding scheme, this rises to between 12 and 65 (depending on the hologram chosen and the method of measuring compression rate) with good decryption and reconstruction quality. Our techniques are suitable for a range of secure three-dimensional object storage and transmission applications.