I have had this done many times; however, none of the folks that I use will do both the body of the shirt and the sleeves for $20, and I live in the Southern U.S. where things are normally less expensive. I usually just have the body of my dress shirts taken in and leave the sleeves since I have a jacket on most of the time I'm wearing one of those shirts. The sleeves just aren't that big of a deal to me. I think the last time I had a shirt done it was $14 to take in the body.

Cruiser

 

Any reasonably competent tailor should be able to do it. My place is less expensive than Cruiser's -- I don't think I've paid more than $25 or so for both sleeves and body. But it varies from shop to shop, of course.

 

any reasonably competent tailor or dressmaker can do this. 25 is a reasonable price for sleeves and sides.
caution if you do the sleeves and make them too narrow it will be uncomfortable bending your elbows. also at the armhole do not take in more than one inch. because it gets snug very fast.

 

Thanks so much all for the advice!

 

I have this done all the time to my dress shirts. I wouldn't take it to the lady at the corner dry-cleaners to have it done, but I would try and find someone who has a good reputation. I usually pay $39 to have the sides and arms taken in (this includes making the armhole smaller), and sometimes take fabric out of the back through the darts. It would probably be $25-$30 or so if I left the back alone.
Granted, Chicago is a big city so things cost a little bit more. I probably pay a little bit more than I have to, but I know my tailor will do it right. The extra $10 or so it worth the peace of mind.