We compress phase-shift digital holograms (whole Fresnel fields) for the transmission of three-dimensional images. For real-time networking applications, the time required to compress can be as critical as the compression rate. We achieve lossy compression through quantization of both the real and imaginary streams, followed by a bit packing operation. Compression losses in the reconstructed objects were quantified. We define a speedup metric that combines space gains due to compression with temporal overheads due to the compression routine and the transmission serialization. We empirically verify transmission speedup due to compression using a special-purpose Internet-based networking application. (C) 2003 Optical Society of America.