I don't think they go high enough to prevent them from rolling down enough. They cut you off in the middle of the torso where you're trying to hide some belly, so the muffin top created can cause it to roll down more. I don't think these are super tight and could stand to be tighter for more compression (I followed the size chart and actually am on the larger end of the range), but they are comfortable. The fabric is very soft and smooth and it doesn't dig into the body.
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