Digital holography is a successful technique for recording and reconstructing three-dimensional (3D) objects. The recent development of megapixel digital sensors with high spatial resolution and high dynamic range has benefited this area. We capture digital holograms (whole Presnel fields) using phase-shift interferometry and compress then to enhance transmission and storage efficiency. Lossy quantization techniques are applied to our complex-valued holograms as the initial stage in the compression procedure. Quantization reduces the number of different real and imaginary values required to describe each hologram. We outline the nonuniform quantization techniques that we have had some success with thus far, and present our latest results with two techniques based on companding and histogram approaches. Companding quantization attempts to combine the efficiency of uniform quantization with the unproved performance of nonuniform quantization. Our results show that companding techniques can be comparable with k-means and neural network clustering algorithms, while only requiring a single-pass processing step. In addition, we report on a novel lossy compression technique that utilizes histogram data to quantize digital holograms. Here, we use the results of a histogram analysis to inform our decision about the best choice for quantization values.