Several extraction systems based on functionalized calixarenes in mixed fluorinated diluents were examined. Technological flowsheets for radioactive waste processing with these extraction systems were developed and tested. It is shown that under the selected conditions one can achieve decontamination factors from cesium isotopes and alpha-emitters, sufficient for converting high-level waste of the "Mayak" Production Association into the low-level category with the subsequent possibility of their disposal at near-surface sites.