Methods are described for the removal of highly soluble radioactive anions, e.g., radioactive technetium and/or radioiodide, from an aqueous solution. The methods utilize a sequestering agent that includes an organoclay, i.e., a clay with an intercalated cationic quaternary amine, as a sorbent for highly soluble radioactive anions that are present within an aqueous solution. In exemplary embodiments, the method can be utilized to treat aqueous waste at a nuclear power facility or to treat a groundwater contamination site or a soil or sediment contaminated site.