Ag0.8In2.4Te4 (= AgIn3Te5) and Ag0.5In2.5Te4 (= AgIn5Te8) form solid solutions with CdIn2Te4, which are interesting as materials for photovoltaics or with respect to their thermoelectric properties. The corresponding crystal structures are related to the chalcopyrite type. Rietveld refinements of high-resolution synchrotron powder diffraction data measured at K-absorption edges of Cd, Ag, In, and Te and electron diffraction reveal the symmetry as well as the element and vacancy distribution in Ag0.8In2.4Te4 (= AgIn3Te5)/Ag0.5In2.5Te4 (= AgIn5Te8) mixed crystals such as Ag0.25Cd0.5In2.25Te4 and Ag0.2Cd0.75In2.1Te4. All compounds of the solid solution series (CdIn2Te4)x(Ag0.5In2.5Te4)1-x exhibit the HgCu2I4 structure type (space group I4̅2m) with completely ordered vacancies but disordered cations. The uniform cation distribution and thus the local charge balance are comparable to that of CdIn2Te4. In contrast, Ag0.8In2.4Te4 (= AgIn3Te5) crystallizes in the space group P4̅2c with disordered cations and partially ordered vacancies. This is corroborated by bond-valence sum calculations and the fact that there is a Vegard-like behavior for compounds with 0.5 < x in the pseudobinary system (CdIn2Te4)x(Ag0.8In2.4Te4)1-x. Owing to the different structures, there is no complete solid solution series between CdIn2Te4 and AgIn3Te5. All compounds in this work are n-type semiconductors with a low electrical conductivity (∼1 S/m) and rather high absolute Seebeck coefficients (up to -750 μV/mK; 225 °C). Electrical band gaps (Eg) determined from the Seebeck coefficients as well as (more reliably) from the electrical conductivity range between 0.19 and 1.13 eV.