Dispersive thin-film stacks are interesting as compact, cost-effective devices for temporal dispersion compensation and wavelength multiplexing. Their performance depends on the total group delay or spatial shift that can be achieved. For general multilayer stacks, no analytic model exists relating the performance to the stack parameters such as the refractive indices and the number of layers. We develop an empirical model by designing and analyzing 623 thin-film stacks with constant dispersion. From this analysis we conclude that, for given stack parameters, the maximum constant dispersion value is inversely proportional to the wavelength range over which the dispersion is achieved. This is equivalent to saying that, for constant dispersion, there is a maximum possible spatial shift (or group delay) that can be achieved for a given material system and number of layers. This empirical model is useful to judge the feasibility of dispersive photonic nanostructures and photonic crystal superprism devices and serves as a first step in the search for an analytic performance model. We predict that an 8-channel wavelength multiplexer can be realized with a single 21-microm-thick SiO2-Ta2O5 thin-film stack.