How can I completely remove wrinkles from a vellum sim?

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Hello,

I am working on a project (can't share the file. I'm sorry) where I am squeezing some spherical objects against a wall.
I am using vellum pressure constraints to simulate it and I am trying to keep the stretching when the squeezing gets too hard, but prevent any wrinkles.
Imagine a bubble that just can't pop, being squeezed extensively against a surface. That's what I'm going for. Lot's of stretching bu no wrinkles.

So far, the stretching is working fine as expected but I am getting wrinkles no matter what.

I tried setting the stretch and bend stiffness to 100e+10, both damping ratios to 0.8, I tried 10 substeps and 3000 constraint iterations on the vellum solver, I even tried using vellum struts and vellum shape match but literally nothing has worked. No matter what I do, I can't get rid of the wrinkles.

What would be your approach to get this effect?

Thank you a lot.
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