(This may be something many of you already know, but I just discovered it)
I was trying to replace the elastic in nylon tricot half slip in the usual manner by quartering the elastic and waist and stitching the elastic to the top edge. Even though I stretched only the elastic and not the tricot, the edge of the knit kept curling. I found that if I marked the waistline a bit lower down (in this case I made a line about 3/4" down from the edge) and placed the elastic at the line I was able to avoid the problem caused by the cut edge curling. I simply zig-zagged the (stretched) elastic and trimmed the excess fabric above after stitching.