What should tsh be to suppress thyroid cancer?

0 to < 0.1: Generally above 0 but less than 0.1, a range that is difficult to achieve and maintain consistently. Use only brand name thyroid replacement.

Close to ZERO: If you are taking ample amounts of thyroid hormone. The idea is that TSH may be able to stimulate cancerous as well as normal thyroid tissue.

TSH should be low.: The TSH should never be elevated in a patient with a history of thyroid cancer. A patient should be maintained on a dose of synthroid (thyroxine) sufficient to suppress the TSH to a level below normal. Otherwise the TSH might stimulate the regrowth of thyroid tissue and possibly thyroid cancer.