In experiments on model membranes, formation of large domains of different lipid composition is readily observed. However, no such phase separation is observed in the membranes of intact cells. Instead, small transient inhomogeneities called lipid rafts are expected in these systems. One of the numerous attempts to explain small domains refers to the coupling of the membrane to its surroundings, which leads to the immobilization of some of the membrane molecules. These immobilized molecules then act as static obstacles for the remaining mobile ones. We present detailed Molecular Dynamics simulations demonstrating that this can indeed account for small domains. This confirms previous Monte Carlo studies based on simplified models. Furthermore, by directly comparing domain structures obtained using Molecular Dynamics to Monte Carlo simulations of the Ising model, we demonstrate that domain formation in the presence of obstacles is remarkably insensitive to the details of the molecular interactions.