This study of bed-load transport was undertaken on the basis of laboratory data in two states, i.e., limit of deposition and deposited bed, by using new design criteria, whereby, compared to earlier similar studies, fewer parameters were considered, yet with almost the same or in some cases an even greater level of accuracy. The modified criterion in the new design for transport in the limit of deposition was using only three dimensionless parameters, i.e., Froude number, volumetric concentration of sediment, and relative size of the grain. But the new design criterion applied to the deposited bed case used four dimensionless parameters, i.e., three parameters used for the preliminary case besides the relative thickness of sedimentation. Compared with other known relationships in sediment transport, the produced equations introduced here yield better results than previous studies. With the lessened number of parameters, the results are much easier to obtain.