Data from 39 flume studies that report equilibrium bed configuration as well as water temperature, flow depth, flow velocity, and sediment size are used to develop the best approximation to the relationships among bed phases (ripples, dunes, lower-regime plane bed, upper-regime plane bed, and antidunes) produced by flows of water over loose sediments. We use a three-axis graph with dimensionless measures of mean flow depth, mean flow velocity, and sediment size along the axes. The relationships are presented as a series of depth-velocity sections and velocity-size sections through the dimensionless diagram. Boundaries between stability fields of the bed phases were drawn as smooth surfaces that minimize misplacement of data points. A large subset of the data, for which reliable values of bed shear stress are reported, was used to represent the stability relationships of the bed phases in a graph of dimensionless boundary shear stress against dimensionless sediment size. The graph shows substantial overlapping of the fields for dunes, upper plane bed, and antidunes owing to the decrease in bed shear stress in the transition from dunes to plane bed with increasing flow velocity. The topology of bed-phase boundaries was guided by the relationships shown in the dimensionless depth-velocity-size diagram.