Optimization of the compositions of Cd1–xRxF2+x nonstoichiometric phases (CaF2 type, R is a rare-earth element) for the ionic conductivity and thermal stability is based on the temperature measurements of the electrical conductivity of single crystals depending on the R3+ ionic radii and RF3 content and on the investigation of phase diagrams of the CdF2–RF3 systems. It is shown that the conductivity of 20 compositions out of 30 studied Cd1–xRxF2+x crystals exceeds the conditional limit σ500K = 10–5 S/cm, below which the use of solid electrolytes in electrochemical devices is believed to be undesirable because of low conductivity. The maximum conductivities σ500K = (3.0–3.2) × 10–4 S/cm and σ293K = (1.5–2.3) × 10–8 S/cm are observed for solid electrolytes with R = Ho, Er, Tm, or Yb and x = 0.22–0.27.