Abstract: Techniques for solving the problem of constructing a Stäckel model by generalizing the potential from the equatorial plane to the entire space are considered. The initial model potentials in the Galactic plane have been derived for three samples of masers based on the catalogs of Reid et al. (2019) and the VERA collaboration (Hirota et al. 2020) by optimizing the model rotation curve. The Stäckel generalization of the initial models is shown to lead to an unrealistic vertical density distribution (a highly flattened halo, an insufficiently flattened disk), irrespective of the database used. Two techniques for solving the problem are considered. In the first (simpler) one, observational constraints have been imposed on the density law in the disk and/or the halo, which has led only to a partial success for the disk (an acceptable, but not arbitrary flattening). In the second (more complex, but more universal) one, the equipotential method has been used to generalize the potential to the entire space. It is shown that this allows the vertical structure of the model to be controlled under the Stäckel decomposition by combining the components of various specified flattening, including the spherical ones, in the model and, hence, solves the problem of taking into account the data on the vertical structure of the Galaxy in Stäckel modeling. A set of physically adapted three-component (a halo, a thin disk, a bulge/thick disk) Stäckel models of the Galaxy has been constructed under various assumptions about the vertical structure of its components by this technique from masers and based on the circular velocity curve from data on luminous red giant stars (Eilers et al. 2019).