Congrats on getting the dose increase you needed!
It seems that doctors who don't suffer with hypothyroidism themselves think we only need adequate FreeT3 levels since T3 is the active hormone.
They fail to realize that certain parts of the body require "fresh" T4 to convert to T3 so, we need adequate stores of T4 (as measured by the FreeT4 level).
Since you are taking desiccated thyroid, you could be like most people and be fine with a FreeT3 level that is proportionately higher in the range than your FreeT4 level.
If your doctor optimizes your FreeT3 level (gets it to the upper third/quarter of the range) and you have ongoing hypo symptoms, that's a sign your FreeT4 level is inadequate. The addition of a small dose of synthetic T4 (levothyroxine) can help in situations such as this.
Dr. Leslie DeGroot, noted endo and co-author of thyroid textbook "The Thyroid and Its Diseases" maintains an online thyroid textbook called "Thyroid Disease Manager".
The section on hypothyroidism mentions the types of levels healthy people have - it make sense that any doctor treating hypothyroidism would try to achieve similar levels for his/her patient.