The modular curve with Gamma₀(p)$-level structure has a beautiful integral model over BZ_p, and generalizations of this model to any Shimura variety with p-parahoric level have been constructed in the last 30 years. When passing from Gamma₀(p)-level to Gamma₁(p)-level, the situation changes drastically. In the talk I will explain a general method that potentially allows to deal with such level structures. The method is based on the construction of torus embeddings of the maximal torus of a reductive group scheme. Joint work with G. Pappas.