Still seems to me like it is related to the size. changing the height to 1 makes it much more stable. @Cedric , do you know of this kind of limitation with ammo?
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Nop, the only limitation I know (which is also the case with other physics engine) is when mixing high values with small ones. Like bodies with very high speed & collision detection.
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It makes it more stable yes, but if you look close enough you can see small vibrations in the mesh no matter how big it is 
Even when the cylinder happens to stand on its top and bottom ends