The Ganges and Brahmaputra are the two largest rivers in Bangladesh. Discharge estimations of these rivers from a stage-discharge relationship or rating curve are crucial for flood warning/control/mitigation and water resources development. So far, logarithmic rating curves have been widely used in Bangladesh. The suitability of semi-logarithmic, polynomial and quadratic rating curves has not been investigated. In this study, all four recognised stage-discharge relationships were examined for the Ganges and Brahmaputra rivers. Unbiased least squares estimators were determined for the segmented logarithmic and semi-logarithmic rating curves. This enhanced their efficiency in inter-and extrapolating discharges from the given river stages. Based on detailed analysis and goodness-of-fit criteria, segmented logarithmic and third order polynomial rating curves were found to be the best for the Ganges and Brahmaputra rivers, respectively.