The selective entrainment of grains by a current from a bed of mixed sizes and densities is important to grain-sorting processes that lead to the formation of placers in sands and to armored beds in gravels. Existing field and laboratory measurements of selective entrainment depart systematically from the standard threshold curves (such as that of Shields) which are based on experiments with nearly uniform grain sizes. Entrainment measurements from beds of mixed sizes form trends which obliquely cross the threshold curves for uniform grains, the crossing point being roughly at the median diameter of the size distribution. Due to this crossover, the coarser size fractions of the distribution require lower-flow stresses for their entrainment than if they formed uniform beds, while the finer-size fractions require higher stresses than uniform beds. With deposits having medians in the range of medium sand through gravel, the larger the individual particle within the mixed sizes, the greater the flow stress required for its entrainment. In this case the smaller grains are preferentially entrained, possibly leading to bed armoring. In contrast, if the median is in the fine-to-medium sand range, the smallest grains in the bed of mixed sizes are the most difficult to entrain due to sheltering by the larger grains; where grain density is also involved, this sorting can lead to the formation of placers. A variety of empirical relationships is considered to quantify the evaluation of selective entrainment from deposits of mixed sizes, but no single formulation is satisfactory for all data sets.