We present the initial results of an ongoing study of higher-order mantle overtones of Rayleigh waves. The main problem is to separate overtone branches (3 R,4 R,5 R), traveling with identical group velocities at similar frequencies. Global stacking is used, both for traveling waves and normal modes, with dispersion results in generally excellent agreement with both theoretical models and values published for a well-separated part of the 3 R branch.