The compound Ag2CdI4 becomes superionic near 388 K as the crystal lattice changes from a tetragonal to a hexagonal structure. Near 445 K, Ag2CdI4 is replaced by an equilibrium mixture of alpha-Agl and CdI2. At each of these phase transitions, ionic conductivity increases by an order of magnitude or more. The substitution of Cu+ for Ag+ in Ag2CdI4 is accompanied by a slight increase in the room temperature conductivity, the result of either increased crystalline defects or an increased Cu+-free volume in the tetragonal lattice. In addition, Cu substitution appears to stabilize the high-temperature, hexagonal structure to temperatures well in excess of 445 K.