and yes, that REALLY makes the fabric straight...it goes along ONE thread in the woof.... do i do this for quilting? no... i tear anything i need to be straight (like borders) but for piecing.... fold (holding the fabric with thumb and forefingers approx a yd apart ON the selvedge sides... straighten this area (by this i mean shift one side of the folded fabric back and forth till the fold on the bottom is straight and flat), pin on both ends of this yard and the straighten the next area, which will be easy as you have begun the straightening. When folded for cutting with no ripples, i trim the end square with the ruler... square to the folded edge and the selvedge...they should be parallel... that's what happens when you get rid of the ripples. now that the end is square... cut your strips and squares and triangles... they will be flat and the right shape... the tiny amount offgrain a small quilt piece is off is simply not pertinent. square up and then cut...they will lay flat and you are working in a few minutes instead of wrestling with a fabric that has been heatset offgrain (or you wouldn't be having problem, and don't kid yourself, they heatset cottons as well as synthetics... it's part of the finishing process) and will take you a ton of time and still will not lay completely flat because you are trying to make it do something it does not want to do....