Compression is essential for efficient storage and transmission of three-dimensional (M) digital holograms. The inherent speckle content in holographic data causes lossless compression techniques, such as Huffman and Burrows-Wheeler (BW), to perform poorly. Therefore, the combination of lossy quantisation followed by lossless compression is essential for effective compression of digital holograms. Our complex-valued digital holograms of 3D real-world objects were captured using phase-shift interferometry (PSI). Quantisation reduces the number of different real and imaginary values required to describe each hologram. Traditional data compression techniques can then be applied to the hologram to actually reduce its size. Since our data has a nonuniform distribution, the uniform quantisation technique does not perform optimally. We require nonuniform quantisation, since in a histogram representation our data is denser around the origin (low amplitudes), thus requiring more cluster centres, and sparser away from the origin (high amplitudes). By nonuniformly positioning the cluster centres to match the fact that there is a higher probability that the pixel will have a low amplitude value, the cluster centres can be used more efficiently. Nonuniform quantisation results in cluster centres that are adapted to the exact statistics of the input data. We analyse a number of iterative (k-means clustering, Kohonen competitive neural network, SOM, and annealed Hopfield neural network), and non-iterative (companding, histogram, and optimal) nonuniform quantisation techniques. We discuss the strengths and weaknesses of each technique and highlight important factors that must be considered when choosing between iterative and non-iterative nonuniform quantisation. We measure the degradation due to lossy quantisation in the reconstruction domain, using the normalised rms (NRMS) metric.