One-dimensional (1-D) methods, namely, coherence method by Ackers (COHM) and exchange discharge method (EDM), and two-dimensional (2-D) method, namely, Shiono-Knight method (SKM) are investigated for computing the discharge capacity of a compound channel. The validity of the methods were tested against previously published experimental data sets. A comparison is made between 1-D and 2-D models, with respect to the accuracy and ease of application for conveyance calculations. It is shown that EDM is able to simulate the measured discharge values more accurately among 1-D methods and also gives less error than 2-D SKM for the data analyzed herein. EDM is hence recommended for estimating the discharge capacity of a compound channel.