A series of experiments was carried out in a two-stage flume having a smooth main channel and smooth or rough floodplains to investigate the reliability and performance of four different one-dimensional methods for computing the discharge capacity of compound channels, namely, the single-channel method (SCM), the divided-channel method (DCM), the exchange discharge method (EDM), and the Ackers method (AM). Additional data from fixed- and mobile-bed compound laboratory channels with smooth and roughened floodplains and of a prototype compound river channel were also used in the computations. The boundary roughness and scale effects associated with the performance of the four methods are also examined. The results show that the EDM and the AM are able to simulate the measured discharge values more accurately than those of the traditional methods, namely, the DCM and the SCM. Although the error in discharge estimation produced by both the AM and the EDM was generally lower than 10% for both smooth and fixed boundaries, it increased up to 20% for mobile boundaries. Overall, the average relative error in discharge estimations using the AM and the EDM was about 5.4% and 7.1%, respectively, with a standard deviation of 6.7% and 6.8%, respectively.