This paper presents a method to determine how much detail of the height stratification of atmospheric parameters can be retrieved from the inversion of spectral lines (and their polarization profiles, when available) via χ2-minimization algorithms. An a priori analysis of the response functions and their correlations permits an evaluation of the optimal number of inversion nodes and their locations. A number of problems of practical interest are studied by applying this method to different photospheric and chromospheric models of quiet Sun and sunspots. As a result of this analysis I obtain the optimal discretization for retrieving the temperature and magnetic field stratifications in such atmospheres. I show that the Fe I lines at 6302 Å provide a height resolution for temperature inversions close to Δτ500~=0.5 in the middle photosphere. In comparison, the chromospheric Hα line allows for a resolution of Δτ500~=1.5 through the chromosphere. This kind of analysis may also be useful in other contexts in which χ2-minimization algorithms are employed.