Fixing these involves replacing the elastic. I ordered some 1 inch wide elastic (the original was 1.5 inches wide, but we will make the 1 inch work). I will also eliminate the useless drawstring.
Somewhat to my surprise, you cut the elastic to fit your waist exactly. This actually makes sense if you have hips. If you are shaped like a watermelon, you will have other issues to solve. Then one method is to join the ends with a scrap of fabric using bar tacks and zig-zag stitches. Then mark the 1/2 and 1/4 way points on the circular piece of elastic.
Take the garment apart using a seam ripper. The elastic is typically enclosed in a 1 or 2 way "hem". When you sew in the elastic, stretch it to match the unstretched fabric. Then when you release it, the fabric will bunch up naturally.
If the existing elastic still has enough life in it, you can partially open up the garment, pull out a loop of elastic and shorten it -- but this is not what I intend to do.
The following videos are good, pretty short, and show the game (and more!) --
Tom's home page / tom@mmto.org