The ModelFest data set was created to provide a public source of data to test and calibrate models of foveal spatial contrast detection. It consists of contrast thresholds for 43 foveal achromatic contrast stimuli collected from each of 16 observers. We have fit these data with a variety of simple models that include one of several contrast sensitivity functions, an oblique effect, a spatial sensitivity aperture, spatial frequency channels, and nonlinear Minkowski summation. While we are able to identify one model, with particular parameters, as providing the lowest overall residual error, we also note that the differences among several good-fitting models are small. We find a strong reciprocity between the size of the spatial aperture and the value of the summation exponent: both are effective means of limiting the extent of spatial summation. The results demonstrate the power of simple models to account for the visibility of a wide variety of spatial stimuli and suggest that special mechanisms to deal with special classes of stimuli are not needed. But the results also illustrate the limited power of even this large data set to distinguish among similar competing models. We identify one model as a possible standard, suitable for simple theoretical and applied predictions.