We propose an approach to spatial modeling of extreme rainfall, based on max-stable processes fitted using partial duration series and a censored threshold likelihood function. The resulting models are coherent with classical extreme-value theory and allow the consistent treatment of spatial dependence of rainfall using ideas related to those of classical geostatistics. We illustrate the ideas through data from the Val Ferret watershed in the Swiss Alps, based on daily cumulative rainfall totals recorded at 24 stations for four summers, augmented by a longer series from nearby. We compare the fits of different statistical models appropriate for spatial extremes, select that best fitting our data, and compare return level estimates for the total daily rainfall over the stations. The method can be used in other situations to produce simulations needed for hydrological models, and in particular, for the generation of spatially heterogeneous extreme rainfall fields over catchments.