We examine how the wavenumber influences the compression in a wavelet boundary element method for the Helmholtz equation. We show that for wavelets with high vanishing moments the number of nonzeros in the resulting compressed matrix is approximately proportional to the square of the wavenumber. When the wavenumber is fixed, the wavelet boundary element method as optimal complexity with respect to the number of unknowns. When the mesh spacing is proportional to the wavelength, the complexity of the wavelet boundary element method is approximately proportional to the square of the number of unknowns.