Sequences of integers which represent the output of a time sampled and quantized information source are considered. If the sequences are known to have first differences less than a given positive integersor if they are known to be monotonic (either increasing or decreasing) and have first differences satisfying the above property, optimal encoding schemes are presented, in terms ofs, the number of samplesm, and the number of quantization levelsq. The encoding schemes are presented as simple algorithms which may be implemented in a special purpose computer on board scientific spacecraft.