Painstaking adjustment of an optimum low-temperature cycle (LTC) condenser temperature allows cascade refrigeration system (CRS) to operate at maximum performance. This study exhibits an original approach because, for the first time, advanced exergy analysis is implemented under an optimum LTC condenser temperature of CRS operating with R41/R1233zd(E) as an environmentally-friendly refrigerant pair. Under the auspices of advanced exergy analysis, there is endogenous exergy destruction of 50.43% and exogenous exergy destruction of 49.57% within total exergy destruction. It is pointed out that the interactions between the CRS components (external irreversibilities) are partly less than exergy destruction that occurs within components (internal irreversibilities). The avoidable part within total exergy destruction, which is greater than the unavoidable part, indicates that components have a high improvement potential with a value of 56.31%. Furthermore, LTC compressor depends significantly on other components, as it has the largest exogenous part of exergy destruction with 75.82%. The results indicate that the CRS’s exergy efficiency, which can be determined based on conventional exergy analysis, is only 36%. However, this increases to 68% with the improvements needed for the components.