Quick Sleeve Alteration

I am quite sure this is not the 'proper' way to alter a sleeve. However, most people don't have the problem that I have: coats with sleeves which are just too short.

A friend of mine gave me two nice coats she was going to give away. Both fit fine except for the sleeve length. So what I did was remove the hem of the sleeve and just sew up the very edge. This is what it looks like now:

As you can see, I need to press the sleeve a bit, but you get the idea: It doesn't look bad from a distance.I did this once with a pair of pants, too. I thought about adding a ruffle or something to make the sleeve longer, but 1) didn't want to spend the time or money to go to the fabric store and 2) didn't think I'd be able to find fabric to match perfectly.

Any other ideas for lengthening sleeves or pant legs?