For many classes of neurons, the relationship between computational function and dendritic morphology remains unclear. To gain insights into this relationship, we utilize an inverse approach in which we optimize model neurons with realistic morphologies and ion channel distributions (of I(KA) and I(CaT)) to perform a computational function. In this study, the desired function is input-order detection: neurons have to respond differentially to the arrival of two inputs in a different temporal order. There is a single free parameter in this function, namely, the time lag between the arrivals of the two inputs. Systematically varying this parameter allowed us to map one axis of function space to structure space. Because the function of the optimized model neurons is known with certainty, their thorough analysis provides insights into the relationship between the neurons' functions, morphologies, ion channel distributions, and electrophysiological dynamics. Finally, we discuss issues of optimality in nervous systems.