This paper presents the results of an attempt to develop a rational approach to the design of a practical digital data compression system. The system analyzed is buffer controlled and compresses data by use of a zero-order floating aperture predictor algorithm. For simplicity of analysis and ease in calculation the data to be compressed is modeled as uniformly distributed Markov data. The approach indicated can be extended to other data sources as well. The optimized system selects a set of compressor thresholds or aperture levels, which minimize the mean-squared error between the transmitter input and reconstructed receiver output data. The optimal policy, for this system, is shown to be a function of the present and past contents of the transmitter's buffer, the buffer length, the number of bits of amplitude resolution, the normalized autocorrelation coefficient of the data, and the transmission ratio. The necessary buffer contents for determination of the optimal policy are the queue length and amplitude of the present and past words in the buffer. After making tradeoffs between mean-squared error and buffer size, the optimized system can be implemented with low hardware cost due to the small buffer lengths required.