A method of producing an impure argon-rich stream (174, 195) in a cryogenic air separation plant, the method comprising the steps of: (a) directing a flow of compressed and purified feed air into a higher pressure column configured to produce an oxygen-enriched liquid and a nitrogen-rich stream by cryogenic rectification within the higher pressure column; (b) withdrawing the nitrogen rich stream from the higher pressure column and directing it to a lower pressure column configured to produce an oxygen product stream and a nitrogen waste stream and optionally a nitrogen-rich product stream by cryogenic rectification within the lower pressure column; (c) directing an argon-oxygen containing vapor stream from the lower pressure column to an argon rectification column (56, 90) disposed within the lower pressure column, the argon rectification column configured to produce an impure argon-rich vapor stream having oxygen impurities and an oxygen-rich bottoms liquid by cryogenic rectification within the argon rectification column; (d) directing the oxygen-rich bottoms liquid from the argon rectification column to the lower pressure column; (e) directing a portion of the impure argon rich vapor stream to an argon condensing assembly disposed within the lower pressure column at a location above the argon rectification column; (f) withdrawing the oxygen-enriched liquid from the higher pressure column, combining it with a portion of down-flowing liquid in the lower pressure column to form a combined stream as a boiling side fluid, and directing the combined stream to the argon condensing assembly, the argon condensing assembly configured to condense the impure argon-rich vapor stream against the boiling side fluid to produce an impure argon-rich liquid stream and a partially vaporized oxygen-rich stream; (g) passing the partially vaporized oxygen-rich stream from the argon condensing assembly into the lower pressure column; and (h) removing the impure argon-rich liquid stream from the argon condensing assembly disposed within the lower pressure column as an argon rejection stream; wherein the argon rejection stream contains between about 4% and 25% of oxygen impurities. (a) directing a flow of compressed and purified feed air into a higher pressure column configured to produce an oxygen-enriched liquid and a nitrogen-rich stream by cryogenic rectification within the higher pressure column; (b) withdrawing the nitrogen rich stream from the higher pressure column and directing it to a lower pressure column configured to produce an oxygen product stream and a nitrogen waste stream and optionally a nitrogen-rich product stream by cryogenic rectification within the lower pressure column; (c) directing an argon-oxygen containing vapor stream from the lower pressure column to an argon rectification column (56, 90) disposed within the lower pressure column, the argon rectification column configured to produce an impure argon-rich vapor stream having oxygen impurities and an oxygen-rich bottoms liquid by cryogenic rectification within the argon rectification column; (d) directing the oxygen-rich bottoms liquid from the argon rectification column to the lower pressure column; (e) directing a portion of the impure argon rich vapor stream to an argon condensing assembly disposed within the lower pressure column at a location above the argon rectification column; (f) withdrawing the oxygen-enriched liquid from the higher pressure column, combining it with a portion of down-flowing liquid in the lower pressure column to form a combined stream as a boiling side fluid, and directing the combined stream to the argon condensing assembly, the argon condensing assembly configured to condense the impure argon-rich vapor stream against the boiling side fluid to produce an impure argon-rich liquid stream and a partially vaporized oxygen-rich stream; (g) passing the partially vaporized oxygen-rich stream from the argon condensing assembly into the lower pressure column; and (h) removing the impure argon-rich liquid stream from the argon condensing assembly disposed within the lower pressure column as an argon rejection stream; wherein the argon rejection stream contains between about 4% and 25% of oxygen impurities.