Two novel compounds, K2Cu3(SO4)4 and KNaCu(SO4)2, were synthesized. The crystal structure of K2Cu3(SO4)4 is based on a [Cu3(SO4)4] framework with relatively simple bond topology, but with four different CuO n polyhedron geometries. The K cations reside in the pores of the framework. The [Cu(SO4)2] framework in KNaCu(SO4)2 encloses large elliptical channels running along [001]. Larger channels are occupied by K, whereas smaller ones are filled by Na. The bond-valence energy landscape (BVEL) approach has been demonstrated to be a useful method for the prediction of the mobility of alkali metal ions in various structures. By means of this approach, the threshold energies at which isosurfaces begin to percolate as well as the directions of possible ion migration in the structures were determined. The modelling of ion migration maps by the analysis of the procrystal electron-density distribution was used to rapidly identify ion migration pathways and limiting barriers between particular crystallographic sites in the structures under consideration. Its consistency and complementarity with the BVEL method have been demonstrated. Both approaches revealed a relatively low ion threshold percolation and migration barriers in the cryptochalcite-type structures [cryptochalcite: K2Cu5O(SO4)5]. Hence, one may assume that its 3D framework type is suited for ion transport applications. The review of all known members of the groups of anhydrous copper sulfates did not reveal a correlation between the porosity of the framework structures and a manifestation of ion conduction properties.