Keep this thought in your mind when you see your shrink...

Sinequan (doxepin) hasn't been used for depression for over 2 DECADES. I would not expect that any current shrink would understand this drug.

It originally came out as a "me-too" to compete with Elavil and Pamelor. That was long before SSRIs came out or the SNRIs which were later.

Today, Elavil (amitriptyline) and Pamelor (nortriptyline) and Doxepin (Sinequan) are now used for pain management, nerve damage in those with neuropathies ( in low subtherapeutic doses). Shrinks as a rule do not treat PNs so they are not aware of these drugs for the most part anymore.
The new Silenor is being detailed to them now for sleeping. Its dose is way below the doses shrinks used for depression treatments.

You will have to be calm and clever and ask for what you want based on your net research so far. If you leave this totally in the lap of your shrink, you may get NOTHING, because they are narrow and protective of their liability. If they don't know this drug and how it works, they will not give you what you are asking for. The bottom line is Sinequan brand = doxepin=Silenor. The only factor here is 4 measly milligrams which is below the therapeutic index for doxepin as an antidepressant.

And as an antidepressant, and a member of the tricyclic family of drugs, it may just cause a tolerance after a couple of months.
Keep that in mind too.

Good luck.