A new series of organic superconductors is reported: lambda-type salts of bis(ethylenedithio)tetraselenafulvalene (BETS) with mixed halide gallium anions. Their preparation and properties are described, with particular emphasis on the electrical resistivity. A strong correlation is observed between the superconducting transition temperature T-c and the unit cell volume, which should enable the superconducting transition to be investigated systematically and facilitate the design of new organic superconductors with enhanced T-c.