By getting rid of the night dose first, I dont simply mean cutting it out, although if you raise your morning dose you might be able to do that.
I meant when you are tapering slowly, always try to reduce the night dose first, and the morning dose last. If you are still having symptoms you can take a small dose like the 1-2mg because that might be just enough to get you through the night, but preferably you would have no night dose.
Basically, when you take prednisone at night, your body has cortisone in the morning and wont attempt to make its own cortisone. When you "starve" your body a bit in the morning for cortisone, its more likely to try to "wake up" your adrenal glands. Thats why its better to get rid of the night dose first, so your body can start making its own cortisone again. Unfortunately when you are "starved" for cortisone thats when you can feel the symptoms, so its best to just go real slow.
Say if you take 6 in the morning and 6 and night now, you could try taking 10 in the morning and only 2 at night, etc. That way your big dose is in the morning and maybe that will help your sleep patterns, but the 2mg at night should hold you over until the morning's dose so you dont feel the withdrawal type symptoms. You might also consider making it an afternoon dose, taking it around lunchtime instead.