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The dose at stated in post #3 is recommended at 25:1 zinc:copper, hardly what could be considered a high copper dose.
•Long-term consumption of zinc in excess of the tolerable upper intake level (40 mg/day for adults) can result in copper deficiency. (More information)
Linus Pauling Institute at Oregon State University
The major consequence of long-term consumption of excessive zinc is copper deficiency. Total zinc intakes of 60 mg/day (50 mg supplemental and 10 mg dietary zinc) have been found to result in signs of copper deficiency. Copper deficiency has also been reported following chronic use of excessive amounts of zinc-containing denture creams (>2 tubes per week containing 17-34 mg/g of zinc; (100)). In order to prevent copper deficiency, the U.S. Food and Nutrition Board set the tolerable upper intake level (UL) for adults at 40 mg/day, including dietary and supplemental zinc (5).
Linus Pauling Institute at Oregon State University
Zinc reduces the amount of copper your body absorbs, and high doses of zinc can cause a copper deficiency. For that reason, many doctors recommend that you take 2 mg of copper along with a zinc supplement.
Zinc | University of Maryland Medical Center