Welt seam
A welt seam resembles a flat-felled seam but is less bulky. Rather than folding over and pressing the “top” seam allowance, it is simply finished with a serger, zigzag stitch or pinking shears and then stitched down. It provides a nice look on the inside of garments, especially on fabric like this that shreds madly. (This view is from the wrong side.)
Supplies

The Process
Sew your regular seam, right sides together.
I like to press the seam open first so I can work on either side of the seam allowance.
Finish the left side of the seam allowance. You can serge it or zigzag (as I did here), or even use pinking shears. This fabric is really “shreddy,” so it didn’t respond well to pinking shears.
Trim the right side seam allowance down.
End result is this. Now press both seam allowances to the right so that the finished seam allowance is covering up the trimmed one.
Stitch down the front side of the fabric, catching the finished seam allowance on the back. I sewed about 1/4″ from the original seam. I picked lime green thread so it would stand out, but it’s still a bit hard to see.
This is how it looks from the back. That seam allowance is stitched down and secured.