Although invasion risk is expected to increase with propagule pressure (PP), it is unclear whether PP-invasibility relationships follow an asymptotic or some other non-linear form and whether such relationships vary with underlying environmental conditions. Using manipulations of PP, soil fertility and disturbance, we tested how each influence PP-invasibility relationships for Lespedeza cuneata in a Kansas grassland and use recruitment curve models to determine how safe sites may contribute to plant invasions. After three growing seasons, we found that the PP-invasibility relationships best fit an asymptotic model of invasion reflecting a combination of density-independent and density-dependent processes and that seeds were aggregated within the plant community despite efforts to uniformly sow seeds. Consistent with some models, community invasibility decreased with enhanced soil fertility or reduced levels of disturbance in response to changes in the fraction of safe sites. Our results illustrate that disturbance and soil fertility can be a useful organizing principle for predicting community invasibility, asymptotic models are a reasonable starting point for modeling invasion, and new modeling techniques—coupled with classic experimental approaches—can enhance our understanding of the invasion process.