Re-using wool from a sweater?

Is it possible to re-use the wool from a handknitted sweater to make another hand-knitted sweater? Is there anything you can use to treat the wool to make it knit up well? My Mum usually unpicks old sweaters and turns them into throws, but has requested that I 'ask the internet' whether there's some way of making the re-used wool knit up more easily.

Start by eliminating wool from worn areas where the yarn has worn thin. If the yarn has got too "fluffy" because it has been rubbed, it may be weaker even if it is not thin. You can get fluffy wool to run more smoothly when knitting it, by passing it through a round or few of wax. Cut a candle into rounds and remove the wick by pulling it out, and then thread the yarn through the central holes. It will get waxed as it passes through, and run a little easier through your hands and the needles.
Washing the unpicked wool helps to remove the kinks too.

Hi, my friend used to do just this when her kids were little. As stated above, discard any rubbed or worn areas. Wind the unpicked wool around the phone book or something similar to make hanks out of. Then wash them in a good quality wool wash and let dry before winding into balls. This will remove most of the kinks and make it much nicer to re knit.
My friend never bothered with the waxing bit as she only unpicked smooth wool rather than fluffy.

My Mum used to do this all the time. She would buy old jerseys from the op shop, unpick them and re-use the wool. As you can imagine, we had some very colourful woollen items in our house!

Mum used to take the item apart at the seams, unpick the wool and wrap it around the back of a chair so it ended up as a big, loose skein. Then she would hand-wash it using pure soap flakes and squeeze it in a towel to dry.

Then when the wool was still slightly damp, she would re-wind it around the chair back and leave it there to dry thoroughly. That would get rid of most of the kinks. After the wool was dry and unkinked she would then roll it into balls ready to use.

Of course all this is much easier if you have access to child slave labour.