This experimental investigation examined the controls on the geometry of cross-sets formed by subaqueous dunes. A range of steady, unidirectional flow conditions spanning the field of dune existence was investigated, and aggradation rate ranged from 0 mm s−1 to 0·014 mm s−1. Data from an ultrasonic depth profiler consist of high-resolution temporal and spatial series of bed profiles from which dune height and length, migration rate and the depth of trough scour were measured. Cross-set thickness and length were measured from sediment peels. The size and shape of dunes from an equilibrium assemblage change continuously. Individual dunes commonly increase in height by trough scouring and, occasionally, by being caught-up by the upstream dune. Both types of behaviour occur suddenly and irregularly in time and, hence, do not appear to depend on dunes further upstream. However, dune climbing or flattening is a typical response of dunes that disappear under the influence of the upstream dune. All types of behaviour occur at any flow velocity or aggradation rate. Successive dune-trough trajectories, defined by dunes showing various behaviours, affect the geometry of the preserved cross-sets. Mean cross-set thickness/mean dune height averages 0·33 (±0·7), and mean cross-set length/mean dune length averages 0·49 (±0·08), and both show no systematic variation with aggradation rate or flow velocity. Mean cross-set thickness/mean cross-set length tends to decrease with increasing flow velocity and Froude number, therefore allowing a qualitative estimation of flow conditions. Quantitative analysis of the temporal changes in the geometry and migration rate of individual dunes allows the development of a two-dimensional stochastic model of dune migration and formation of cross-sets. Computer realizations produced stacks of cross-sets of comparable shape and thickness to laboratory flume observations, indicating a good empirical understanding of the variability of dune-trough trajectories. However, interactions among dunes and aggradation rates of the order of 10−2 mm s−1 should be considered in future improved models.