We report a new coding phenomenon in multi-terminal information theory. In particular, we show that for distributed source coding involving two sources, as the block-length of the code is increased, the performance improves initially, but plateaues, and then decreases. The best performance is achieved for some finite block-length that depends on the source distribution. To achieve the same performance, the standard Berger-Tung approach requires multi-letterization. This explains why for distributed source coding, single-letter inner bound of Berger and Tung is not optimal which was recently established using an alternate argument based on continuity. The new approach leads to new computable characterization of performance limits. We explore application of this approach in other problems.