We thank Faccioli, Vanini, Paolucci, and Stupazzini for their interest in our articles (Bielak et al. , 2003; Yoshimura et al. , 2003; hereafter I and II). We will refer to their comments (Faccioli et al. , 2004) as fvps. The primary aim of fvps is (1) to illustrate the implementation by fvps of the domain reduction method (drm) described in I and II for the hybrid finite-element–spectral-element (fe–se) method, and (2) to show that the use of ses can lead to dramatic reduction in computer processing unit (cpu) time and storage requirements, without loss of accuracy, with respect to the traditional fes used in II. We will show (1) that since the fe–se method is a particular case of the fe method (fem), the drm described in I and II, and in our earlier work (Loukakis, 1988; Loukakis and Bielak, 1994), provides the complete theoretical framework needed for the application of the drm to fe–ses, and, thus, the section titled “Method” in fvps is essentially redundant; and (2) that while ses are ideally suited for problems in which the exact solution is smooth within every se, the advantages of the se method (sem) over other methods for problems that exhibit discontinuities and singularities is far from having been demonstrated. To our knowledge, there is no evidence thus far that the sem is superior to the fem for every possible wave propagation problem in elastodynamics, since each method has its advantages and disadvantages. We will argue that, in fact, the more traditional fem has important advantages over the particular sem implementation by fvps, and that, most likely, it is more efficient than their sem implementation for realistic, multiscale problems in ground motion simulations that involve large, complex geological structures with …