In this first part of this two part paper, attention is paid to the one-compressor cascades with minimal exergy loss due to mixing of streams with different compositions. The desire to avoid mixing losses leads to the development of several new binary gas separation process schemes with no exergy losses due to mixing of streams with different compositions. These schemes are simulated and compared with the "series type two unit separation cell" for higher purity/recovery separations, and with other conventional schemes for enrichment or rejection of the mon permeable component. These comparisons show that schemes with no mixing losses are much more efficient than conventional schemes in most cases, although they are only marginally more efficient for low pressure side feed schemes with high permeate purity requirements.