A method for flexible production of argon from a cryogenic air separation unit is provided. The disclosed cryogenic air separation unit is capable of operating in a ‘no-argon’ or ‘low-argon’ mode when argon demand is low or non-existent and then switching to operating in a ‘high-argon’ mode when argon is needed. The recovery of the argon products from the air separation unit is adjusted by varying the percentages of dirty shelf nitrogen and clean shelf nitrogen in the reflux stream directed to the lower pressure column. The cryogenic air separation unit and associated method also provides an efficient argon production/rejection process that minimizes the power consumption when the cryogenic air separation unit is operating in a ‘no-argon’ or ‘low-argon’ mode yet maintains the capability to produce higher volumes of argon products at full design capacity to meet argon product demands.