If total T4 is high, and TSH is not going low- the most common reason is that thyroid binding globulin is high. That happens usually due to certain medicines like oral contraceptives or pregnancy is a common condition.

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If you are on thyroid medications, it can lead to high normal T4. Certain other medications like estrogen, biotin etc can also raise T4. Nothing to worry, but if you want more clarification you can do a Free T 4 assay

Hello.. If u already on any thyroid supplement such mild high T4 is very normal when u test after taking tablet.. If u are not previously on any thyroid supplements this can still normal as total T4 levels depends on TBG levels, and active hormone is Free T4.... So no need to worry.. If u are more concerned u can get checked Free T4 levels....!!!!