Duret, you and I must have different definitions of what a "mini" u-lock is. I have several mini u-locks, and none of mine is large enough to go around my rear tire and wheel, plus my seat tube, plus a beefy concrete post set in concrete.

Perhaps your bike has very thin tires, very thin rims, and your tire is rubbing up against a very thin seat tube. But, more likely, you are not locking up to large, beefy steel poles...poles that as thick as the end of a baseball bat, not skinny poles the diameter of a broom handle.

After you have seen the remains of a bike where the crook used the "lift and twist" method and attempted to use the frame of the bike to break the u-lock, you will never put a u-lock around any part of your frame again. But, live and learn.