Compress-forward (CF) schemes are studied in general networks. The CF rate for the one-relay channel defines outerbounds on both the CF rate for general networks and the compression rate-vector region supporting this rate. We show the outerbound is achievable using regular decoding with constant encoding delays, avoiding the exponential delays and restrictions on bidirectional communication in noisy network coding and backward decoding. The concept of layering is introduced to harmonize regular CF schemes with the framework of flow decomposition in the decode-forward setting. Layerings correspond to regular decoding schemes. Any desired compression rate-vector in the outerbound is achievable by some layering, which is found using the same "shift" operation in flow decomposition. In separate work, we show that "shifting" minimizes the operations needed to find layerings and thus minimizes the complexity of the compression rate-vector region.