This disclosure discusses the problems associated with the design, layout, and construction of units and equipment in air separation units. The invention of this disclosure provides a process and apparatus using multiple discrete subcoolers (12, 14). The nitrogen stream (10) exiting the cryogenic distillation columns cools streams (20, 22, 24, 26) in the subcoolers. By having at :.east two subcoolers, the size of the nitrogen vent (nitrogen waste or product stream) can be reduced. This saves fabrication costs and improves reliability by reducing thermal stresses in the piping and equipment. Subcoolers cool rich liquid, lean liquid, liquid oxygen, and/or liquid air streams coding from the main heat exchanger (8) or a system of separation columns. The disclosure also discusses integration of the subcoolers with the main heat exchangers.