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A systematic design method is developed for current leads in practical HTS power systems, where the electric current varies considerably with time. If the current leads are designed on a basis of projected peak current, the conductors may be thermally safe, but must yield an additional cooling load which could be reduced if the lower current level had been considered. On the other hand, the conductor can be optimally sized to minimize the cooling load if a projected current model is given as function of time. But this design causes an overheating of conductor when the current is excessive. This paper presents a quantitative design process of constrained optimization by considering thermal safety and cooling efficiency at the same time. The conductor dimensions are determined to minimize the cooling load with a constraint that the peak temperature should not exceed a given allowed maximum. Based on Wiedemann-Franz approximation, a simple and useful formula is used to explicitly calculate the peak temperature. A step-by-step process of the constrained optimization is presented and demonstrated with examples.