I have seen patients who were doing well on thyroid pills -- Armour, Naturethroid, synthetic -- who have their symptoms and signs under control, but then reduced their thyroid dose on the basis of limited thyroid blood testing which can result in getting the wrong advice leading to a worsening of their symptoms and overall condition, sometime dramatically. This happens because the thyroid testing is usually not as complete as possible (due to financial/insurance restrictions). To be accurate, testing should look carefully at Free T4 and Free T3 levels, Total T4 and Total 3 levels, and TSH and the two common thyroid antibodies. Top university laboratory experts cannot agree as to which of these types of tests is the most accurate; therefore, in difficult cases it is helpful to check all of them.
Without the proper appropriate lab data it is hard to adjust the thyroid dose correctly. The lab tests themselves have a wide normal range so the interpretation of the labs by the doctor should optimally include some clinical judgment as to how the patient is doing on thyroid in terms of signs and symptoms.