We will discuss several new algorithms for use with the Multiscale Coarse-Graining (MS-CG) method developed by Voth and co- workers. These include: the use of hierarchical basis functions for constructing CG potential functions, the elastic net method for solving the variational problem of MS-CG, and a method for constructing three-body CG potentials. We also discuss some necessary conditions for the accuracy of MS-CG potentials and discuss how to construct CG models that satisfy these conditions.