gillyo

I make wall quilts and always sew a line of buttons on the back of the bottom edge. The extra weight
keeps it flush to the wall and as long I make sure it's square it hangs beautifully. For competition quilts I blanket stitch seed beads onto the bottom raw edge before sewing on the binding. You can't see or feel them and the added weight helps it to hang straight.
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Those who make show quilts construct them differently so they'll hang straight. There are a lot of tailoring techniques you can use to make that happen. The fact is that "big time" quilters are highly skilled and have their secrets, I guess that's why they win the big prizes.

Mdegenhart

A big part of lying flat is squaring up your quilt properly.

QuiltE

Exactly MDegenart!............. and that starts with doing so with every seam,
every block, and every step along the way!

bearisgray

In my opinion, that starts with soaking/washing and then drying and ironing/pressing the fabric before cutting it -
and then continues with accurate cutting.

KalamaQuilts

Well, lets get the cotton bolls involved gotta start right, at the source.

I've read interviews by several big show winners that they've made their quilts two and three times to get to the level of perfection they are aiming for.

bearisgray

I suppose the quality of the raw cotton might make a difference - - -

I think I read somewhere that "cotton grown in _____" is the best in the world. Don't remember where that somewhere was, though.