Quite often people with hypothyroidism don't feel well until their TSH (thyroid stimulating hormone) is below 1 or even below the normal range. This is because TSH responds differently to external thyroid hormones (in the form of tablets etc) than it does to the thyroid hormones that our own thyroid produces. Many doctors don't realise this and seem quite happy to stop increasing the dose as soon as TSH is below 5 or 4.5 or whatever the maximum of the "normal" range is.
TSH is higher if you don't have enough thyroxine and other thyroid hormones, and goes very low if you have too much thyroid hormones. Doctors get scared if your TSH goes low because they think you must be getting too much thyroid hormone, but this is rarely the case, unless you are having symptoms of too much thyroid hormone.
I hope that makes sense. You may want to look at the main Thyroid UK website for more information on the thyroid.
I hope that helps.