In analyzing genetic linkage data it is common to assume that the locations of crossovers along a chromosome follow a Poisson process, whereas it has long been known that this assumption does not fit the data. In many organisms it appears that the presence of a crossover inhibits the formation of another nearby, a phenomenon known as "interference." We discuss several point process models for recombination that incorporate position interference but assume no chromatid interference. Using stochastic simulation, we are able to fit the models to a multilocus Drosophila dataset by the method of maximum likelihood. We find that some biologically inspired point process models incorporating one or two additional parameters provide a dramatically better fit to the data than the usual "no-interference" Poisson model.