A method is proposed to approximately compute the seismic response of shallow three-dimensional (3D) alluvial valleys. It is based on the exact solution for a simple configuration. Namely, the antiplane response of a rectangular deposit with a moving rigid base. In such a solution, which is used as a framework for our approximations, the spectral signature of locally generated surface waves is explicit. Thus, an approximate expression is constructed to separately account for one-dimensional (1D) response and lateral effects. Results are presented for two- and three-dimensional cases. Comparisons are provided with rigorous solutions as well. Our formulas allow for fast computations.