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Abstract Notwithstanding the large number of studies on bedforms such as dunes and antidunes, predicting equilibrium bedform type and geometry for a given flow regime, sediment supply and caliber remains an open problem. Here, we present results from laboratory experiments specifically designed to study how upper regime bedform type and geometry vary with sediment supply and caliber. Experiments were performed in a sediment feed flume with flow rates varying between 5 and 30 l/s and sand supply rates varying between 0.6 and 20 kg/min. We used both uniform and non‐uniform sands with geometric mean diameters varying between 0.22 and 0.87 mm. Analysis of our data and data available in the literature reveals that the ratio of total (bedload plus suspension) volume transport rate of sediment to water dischargeQ_s/Q_wplays a prime control on upper regime equilibrium beds. Equilibrium bedforms transition from washed out dunes (lower regime) to downstream migrating antidunes (upper regime) forQ_s/Q_wbetween 0.0003 and 0.0007. For values ofQ_s/Q_wgreater than 0.0015, the bedform length increases withQ_s/Q_w. At these high values ofQ_s/Q_w, equilibrium in fine sand is characterized by upstream migrating antidunes, cyclic steps, and significant suspended load. In experiments with coarse sand, equilibrium is characterized by plane bed with bedload transport in sheet flow mode. Standing waves form at the transition between downstream migrating antidunes and upstream migrating bedforms.