Most quantitative descriptions of neuronal dendrite morphology involve tabulations of measurements and correlations among them. The present work is an attempt to extract from such data a parsimonious set of parameters that are sufficient to describe the quantitative features of individual and pooled dendrites, including their statistical variability. A relatively simple stochastic (Monte Carlo) model was devised to simulate branching dendritic trees. The necessary parameters were then derived directly from measurements of 64 completely reconstructed dendrites belonging to six gastrocnemius alpha- motoneurons, labeled by intracellular injection of HRP. Comparison of actual and simulated dendrites was used to guide the process of parameter extraction. The model included only two processes, one to generate individual branches given their starting diameters and the second to select starting diameters for the daughter branches produced at dichotomous branching points. The stochastic process for branch generation was controlled by probability functions for branching (Pbr) and for terminating (Ptrm), together with a constant rate of branch taper. All model parameters were fixed by motoneuron measurements except for branch taper rate, which was allowed to vary within limits consistent with observed taper rates in order to generate the appropriate total number of branches. The simplest model (model 1), in which Pbr and Ptrm depended only on local branch diameter, produced simulated dendrites that fit many, but not all, characteristics of actual motoneuron dendrites. Two additional properties produced significant improvements in the fit: (1) a small but significant dependence of daughter diameters on the normalized starting diameter of the parent branch, and (2) a dependence of Pbr and Ptrm on distance from the soma as well as on local branch diameter. The process of developing this model revealed unsuspected relations in the original data that suggest the existence of fundamental mechanisms for morphological control. The final model succinctly describes a large amount of data and will enable quantitative comparisons between the dendritic structures of different types of neurons, regardless of their relative sizes.