The aviation sector contributes substantially to global transportation energy use, underscoring the critical need for improving energy efficiency in propulsion systems. Conventional energy-based evaluations can sometimes yield misleading results; therefore, exergy-based analysis provides a more realistic understanding of how energy is utilized and degraded within such systems. In this study, a jet engine is analyzed using exergy efficiency as a principal criterion, with specific attention to the effects of compressor pressure ratio and flight altitude. The investigation identifies an optimal operating point that corresponds to the most effective pressure ratio, which also governs engine sizing. The point where the thrust and exergy efficiency curves intersect is proposed as the optimal design condition. Moreover, the role of nozzle efficiency is examined under a range of flight scenarios. The results indicate that at the optimal design points, specific fuel consumption can be reduced by as much as 22.27% at sea level and 13.43% at cruise altitude when compared to maximum thrust conditions. These design points feature lower compressor pressure ratios than those at maximum exergy efficiency, thus improving practical feasibility for real-world applications. Enhancing nozzle efficiency further improves overall engine performance. For instance, at cruise altitude, increasing flight velocity from 100 to 200 m/s and raising nozzle efficiency from 60% to 100% increases thrust by approximately 33–39% and exergy efficiency by 68–71%. At sea level, these improvements reach up to 41% and 73%, respectively. The findings offer valuable insights into achieving concurrent optimization of thrust and exergy efficiency, providing a practical framework for future propulsion and advanced energy system designs.