When I was putting stuff away earlier I noticed a T shirt that I hadn't worn for ages so I thought I would give it a go with some of the bargain fabric I bought a couple of weeks ago.
Because I overlocked around the neck I didn't need to face it, I just turned it under a small amount and hemmed and it lays nice and flat. I did make sure I pulled on the cotton a little as I overlocked it just to give it a little bit of give as I went around the curve.
Now I didn't put the neckline back the same as on a T shirt as I like the neck a little lower but you could do this if you unpick it carefully first. The sleeves proved to be a pain as I made the mistake of cutting the hem off them to shorten, well even after overlocking the jersey had so much bounce the hem would not lay flat. Then on unpicking one I made a little hole and had to re-cut new short sleeves from the remaining fabric I took from the middle of the shirt. I made sure I cut at the bottom though where the original hem had been so I didn't have problems with that again.
So if you do this and want to change the sleeve length I would recommend taking out the sleeve at the shoulder and shorten from the top or use a binding at the hem.
Here is what the T shirt looked like to begin with, |I think I may repeat this process on more old stuff, and it doesn't require much fabric.