I deconstructed mine first because it was summer and the rubber headgear was hot, and I just didn't like the rubber against my hair. Also, the headgear just sat on my head and wasn't snug enough to be of any support.
For someone who didn't mind the rubber and it fit their head, I think they would do just fine by adding the tights strap directly around the nosepiece for stabilization and leaving it alone.
Pros to deconstructing - lightweight and cool.
Cons to deconstructing - need to pad it so plastic does not sit right on forehead (now using piece of leftover stocking with moleskin - going to switch to a makeup sponge); if not strapped securely it can wiggle and cause leaks.
At first I wound my strap over the upper side of the remaining plastic frame, under the tube, then over the other upper side of the frame. For some reason this quit working for me, so I moved it lower and also add a strap around the nosepiece. Rarely have leaks, and I just let the hose lay across the head of the bed above the pillow and that works fine for me. I have a stocking footie over the nosepiece with 2 slits for the pillows so that the plastic doesn't touch my face.
It's not pretty, but it's comfy.