The irreversibility minimization method of heat exchanger optimization is extended to include a term to account for the exergy of the material of construction of the heat exchanger. The method permits physically realistic optimization to be conducted with the resulting optimum designs providing conceptually beneficial guideposts, which do not change with time or location. Such optima are in contrast to the optima obtained by presently advocated methods, which on one hand indicate unrealistic infinite area heat exchangers, and on the other hand point to optima that may change dramatically with location and time. Although the analysis presented here does not represent a “cure-all” for heat exchanger analysis (economic optimization is still recommended), it does provide valuable conceptual insights and nonchanging guideposts for optimal design. Accompanying exergetic efficiency expressions using the same type of material exergy term show physically more realistic values than the usual expressions.