Data were collected at 20 single opening bridges for 31 floods. Measured backwater ranged from 0.39 to 3.16 feet (0.12 to 0.96 meters). Backwater computed by the Geological Survey method averaged 29 percent less than the measured and that computed by the Federal Highway Administration method averaged 47 percent less than the measured. Discharge computed by the Geological Survey method averaged 21 percent more than the measured. Analysis of data showed that the flood plain widths and the roughness are larger than those used to develop the standard methods. A method to more accurately compute backwater and discharge was developed. The difference between the contracted and natural water-surface profiles computed using standard step-backwater procedures is defined as backwater. The energy loss terms in the step-backwater procedure are computed as the product of the geometric mean of the energy slopes and the flow distance in the reach. An estimate of the average flow distance in the approach reach was derived from potential flow theory. The mean error was 1 percent when using the proposed method for computing backwater and 3 percent for computing discharge.