Cross strata and planar strata (formed by the migration of ripples and dunes or low-relief bed waves on upper-stage plane beds, respectively) are the most common internal structures in fluvial sands and sandstones. The thickness of cross sets or planar laminae at a given location is controlled by (1) aggradation rate relative to downstream migration rate of bed waves and (2) the succession of bed waves of varying height passing the location. A quantitative understanding of this relationship is now appearing, based on new theory and experimental studies with ripples, dunes, and upper-stage plane beds. In many cases, the effects of control 1 can be ignored. In such cases, only the largest bed waves in a population form cross sets or planar laminae; the ratio of mean cross-set thickness/mean height of formative bed waves is less than 0.4, and the ratio of mean cross-set thickness/mean height of all bed waves is less than 0.5. A simple quantitative model (a modified form of the Paola-Borgman model) is presented for predicting the height distributions of bed waves (ripples, dunes, low-relief bed waves) from the thickness distributions of cross sets or planar laminae. If the aggradation rate is appreciable, more of the smaller bed waves in a population can form cross sets or planar laminae, and the preservation ratios increase (to 1 in the case of supercritical climbing-ripple cross strata). In this case, it is necessary to determine the angle of climb and length of the bed waves in order to use the model to predict bed-wave height distributions.