The traditional version of the Method of Fundamental Solutions is revisited, which is based on using external sources. The sources are defined in a completely automatic way using a quadtree cell system controlled by the boundary of the domain. This results in a spatial density distribution of sources which decreases rapidly when going far away from the boundary. A similar technique is also proposed, when the sources are located along the boundary (which can be automated easily) and the collocation points are moved into the interior of the domain. In this case, the boundary conditions have to be properly redefined at the inner collocation points, This is done by using boundary-controlled quadtrees again. Both techniques can be embedded in a multi-level context in a natural way. The accuracy of the resulting methods are less than that of the traditional Method of Fundamental Solutions, but it is still acceptable. However, the computational cost is more moderate and the problems of singularity and the extremely ill-conditioned matrices are avoided.