Lossy and near-lossless digital hologram compression methods are investigated to compress different complexities of wafer surface structures. In the lossy compression method, we apply row- and column-based uniform downsampling together with spline interpolation, whereas in the near-lossless compression method, we use wavelet local modulus maxima and spline interpolation. Results have shown that the lossy compression method is able to achieve a compression ratio of up to 100 for simpler wafer surface structures than that for complex surface structures. However, the near-lossless compression method is able to yield almost lossless compression even for complex wafer surface structures with a compression of about two. The proposed compression methods are computationally friendly for wafer surface structures as there is no time-consuming iterative computation involved.