The delivery of sediment into basins can readily be studied using process-independent models. The simplest such model is the discrete fractionation model in two dimensions, without erosion. It represents the path down which sediment is delivered as a simple set of discrete steps, and assumes that the sediment is delivered down those steps in a series of discrete events. This model has two parameters – the feed volume and the fractionation coefficient. The feed volume is the volume of sediment fed to the first step in the delivery path, and the fractionation coefficient is the proportion of the sediment reaching a step that is then moved on. Several variants of this model are described here, each involving restrictions on one or both of these parameters. The model has obvious and important applications, but these will be difficult to realize until the problem of parameter estimation has been solved. Fortunately, it seems possible to solve this problem by removing some of the model’s restrictions; these were built into it initially for analytical reasons. Removing these restrictions also makes the model applicable to a wider range of sedimentation systems.