I don't fully cover my cockatiel's cage because she can get night frights too. I have the cover over the top half, and it is dark enough in the apartment at night anyway that she sleeps ok. We keep a nightlight across the room that does provide some light so she can still see her perches, etc.. Not all birds need to be fully covered. Try experimenting with partial covering and see what works. My girl is so funny because when she is ready to really sleep,she will go "upstairs" to the covered, darker part of her cage. Then in the morning, whe she is ready to wake up, she come "downstairs" and begin her good morning calls.

Thanks for the advice!
I leave a nightlight on in my room, now, and now Addie's little chirps have become fussy squeaks, like she wants to get out of her cage or go see Salty, rather than terrified squeaks.

Darby
Aderyn (GCC)
and Salty (budgie)

YOu might try putting the cage in a room with a window, and let the room naturaly get darker as the sun goes down. My GCC is afraid of going from a lit room into a dark room, or the lights suddenly going off, but over all the window trick has taught him tha dark means bed time.