Macroscopic spatial variations in advection velocity lead to an increase in dispersion with increasing travel distance or depth. In soils, this increase goes along with a decrease in decay and sorption of organic substances. We used three different one-dimensional models that make different assumptions about the dispersion process to compare predicted leaching in a 1-m-deep soil profile with layers with different sorption and decay parameters. The first two convective–dispersive models assume that dispersion results from microscopic variations in solute particle velocities that are not correlated across soil layer boundaries. The third model, a stream tube model (STM), assumes that the particle velocity remains constant along its trajectory and is perfectly correlated in different layers. The three models were parameterized to predict the same inert tracer breakthrough curve (BTC) at 1-m depth. The first convective–dispersive model assumes a constant dispersion coefficient (“homogeneous” convection–dispersion equation [CDE]). The second model uses different dispersion coefficients in the different layers (“layered” CDE) to predict the same inert tracer BTCs as the STM at the layer boundaries. Despite similar predictions of inert tracer BTCs, the models predicted different BTCs of reactive substances at 1-m depth. The different predictions by the STM and layered CDE illustrate the importance of the correlation of solute particle velocities in different soil layers. They also point to a fundamental problem related to the use of a CDE with a depth-dependent dispersion to mimic a dispersion process caused by macroscopic variations in particle velocities.