A natural chute in the Niobrara River near Cody, Nebr., constricts the flow of the river except at high stages to a narrow channel in which the turbulence is sufficient to suspend nearly the total sediment discharge. Because much of the flow originates in the sandhills area of Nebraska, the water discharge and sediment discharge are relatively uniform. Sediment discharges based on depth-integrated samples at a contracted section in the chute and on streamflow records at a recording gage about 1,900 feet upstream are available for the period from April 1948 to September 1953 but are not given directly as continuous records in this report. Sediment measurements have been made periodically near the gage and at other nearby relatively unconfined sections of the stream for comparison with measurements at the contracted section. Sediment discharge at these relatively unconfined sections was computed from formulas for comparison with measured sediment discharges at the contracted section. A form of the Du Boys formula gave computed tonnages of sediment that were unsatisfactory. Sediment discharges as computed from the Schoklitsch formula agreed well with measured sediment discharges that were low, but they were much too low at measured sediment discharges that were higher. The Straub formula gave computed discharges, presumably of bed material, that were several times larger than measured discharges of sediment coarser than 0.125 millimeter. All three of these formulas gave computed sediment discharges that increased with water discharges much less rapidly than the measured discharges of sediment coarser than 0.125 millimeter. The Einstein procedure when applied to a reach that included 10 defined cross sections gave much better agreement between computed sediment discharge and measured sediment discharge than did anyone of the three other formulas that were used. This procedure does not compute the discharge of sediment that is too small to be found in the stream bed in appreciable quantities. Hence, total sediment discharges were obtained by adding computed discharges of sediment larger than 0.125 millimeter to measured discharges of sediment smaller than 0.125 millimeter. The size distributions of the computed sediment discharge compared poorly with the size distributions of sediment discharge at the contracted section. Ten sediment discharges computed from the Einstein procedure as applied to a single section averaged several times the measured sediment discharge for the contracted section and gave size distributions that were unsatisfactory. The Einstein procedure was modified to compute total sediment discharge at an alluvial section from readily measurable field data. The modified procedure uses measurements of bed-material particle sizes, suspended-sediment concentrations and particle sizes from depth-integrated samples, streamflow, and water temperatures. Computations of total sediment discharge were made by using this modified procedure, some for the section at the gaging station and some for each of two other relatively unconfined sections. The size distributions of the computed and the measured sediment discharges agreed reasonably well. Major advantages of this modified procedure include applicability to a single section rather than to a reach of channel, use of measured velocity instead of water-surface slope, use of depth-integrated samples, and apparently fair accuracy for computing both total sediment discharge and approximate size distribution of the sediment. Because of these advantages this modified procedure is being further studied to increase its accuracy, to simplify the required computations, and to define its limitations. In the development of the modified procedure, some relationships concerning theories of sediment transport were reviewed and checked against field data. Vertical distributions of suspended sediment at relatively unconfined sections did not agree well with theoretical dist