The compressibility of Schur complement matrices is the essential ingredient for H-matrix techniques, and is well understood for Laplace type problems. The Helmholtz case is more difficult: there are several theoretical results which indicate when good compression is possible with additional techniques, and in practice sometimes basic H-matrix techniques work well. We investigate the compressibility here with extensive numerical experiments based on the SVD. We find that with growing wave number k, the ϵ-rank of blocks corresponding to a fixed size in physical space of the Green’s function is always growing like O(kα), with α∈[34,1] in 2d and α∈[43,2] in 3d.