A synergistic extraction mixture containing chlorinated cobalt dicarbollide (CCD), carbamoylmethyl phosphine oxide (CMPO), and polyethylene glycol (PEG) has been investigated for the simultaneous recovery of cesium, strontium, lanthanides, and actinides from highly acidic media. The extraction properties of this mixture depend on the concentration ratio of the components. For recovery of all major radionuclides, the optimal ratio of [CCD]:[PEG]: [CMPO] = 5:1:1 should be used. The use of diphenyl-N,N-dibutylcarbamoylmethyl phosphine oxide and PEG-400 provides the most efficient recovery of cesium, strontium, lanthanides, and actinides. The possibility of using polyfluorinated ethers, esters, ketones, and sulfones as diluents was examined. Phenyltrifluoromethyl sulfone was the most suitable diluent tested. The use of this diluent allows good extraction properties, chemical and radiation stability, excellent explosion/fire-safety properties, and favorable hydrodynamic characteristics. The extraction of radionuclides from HNO₃ media by mixtures of CCD:PEG:CMPO in phenyltrifluoromethyl sulfone and the subsequent stripping behavior were evaluated.