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The distillation columns of a two-column cryogenic air separation unit (ASU) are responsible for a considerable part of the total ASU inefficiencies. The efficiency of a conventional distillation column can be increased by distributing the reboiler and condenser duties over a larger part of its length. In an ASU, this can be realized by moving the low-pressure column (LPC) down along the high-pressure column (HPC), thus increasing the number of heat-integrated stages (HI stages). We present an assessment of the effect that such an intensification of the heat integration has on the performance of the ASU distillation section, using the entropy production as performance criterion. When keeping the operating pressures fixed, the entropy production in the LPC is replaced by entropy production in the HI stages, without affecting the total entropy production. Reducing the pressure ratio enables a reduction in the LPC entropy production without increasing the contribution of the HI stages. For a probable value of the heat-transfer capacity per stage, increasing the pressure in the LPC results in a decrease of 21% in the total entropy production, while decreasing the pressure in the HPC results in a decrease of 23%. Decreasing the pressure in the HPC when using an opportunistic heat-transfer capacity yields a decrease of 31%. The reductions in entropy production materialize eventually as changes in the required ASU compressor, pump, and expander duties. Compared to the addition of either an additional heat exchanger or an additional distillation column, the use of HI stages seems to be the most promising method for improving the thermodynamic performance of a cryogenic ASU. More-detailed experimental data are required to simulate heat-integrated distillation columns accurately. [ABSTRACT FROM AUTHOR]