I have always used my own homemade chinstrap. I noticed (in my case) the mouth opening was caused by side movement of my jaw when I relaxed and the pillow pushed my chin toward the ceiling. I figured that most marketed chinstraps hold against up and down movement (trying to mouth breathe) but likely not so much side to side. I use an ace wrap, but I have seen pantyhose (or other fabric bands) used to good effect... none of which is something you'd like to be seen wearing outside the bedroom (lol), but I have found the ace wrap easy to ignore once I go to sleep... I just have to make sure it's not wrapped too tight. As a matter of fact, the pressure of it is very comforting, and is part of my nightly ritual, so that by now I feel naked sleeping without it! Also, you may want to touch your bottom molars to the upper set when adjusting so that your teeth interlock and can help stabilize your jaw. I am guessing that nothing that is low profile will provide the necessary support. Have you tried pad-a-cheeks? I have never used them, but they may help your current chinstrap or headgear work better for you. I would have used them by now but the ace wrap works and I just love low-tech solutions
John
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"Death doesn't really worry me that much, I'm not frightened about it... I just don't want to be there when it happens." - Woody Allen
Respironics M Series Auto with A-Flex

, Pressure 9-12cmH2O, Mirage Swift II Nasal pillows, and Ace bandages