For a given wavelet system all the wavelet-Galerkin derivatives have the same size (support). Therefore, optimization does not add anything to the computational cost. The current optimization is unconstrained, least square approximation. The improvement in the dispersion error, or frequency response, is balanced by a reduction in the formal level of accuracy. This probably accounts for the modulation that is observed when the number of grid points per median wavelength is reduced. The use of constrained least square approximation could improve these results. The objective functional is the dispersion error (frequency response) and the constraints are the exactness of the optimized stencil acting on selected low order polynomials (formal order of approximation). The procedure is similar to the design of cosine modulated, perfect reconstruction filter banks.