Another good trick for the thin veins is to put a hotpack on the spot they want to use for blood. I had a phlebotomist once look at my elbows and say that neither was gonna work, even with a butterfly. She whipped out one of those instant hotpacks and put it in my elbow, said "Don't leave!" and came back a few minutes later.
The elbow was much more sensitive, but the heat made the vein big enough she could get it. I only had a little bruise from that one.
Also try drinking extra water for the hour before the draw to avoid any possible dehydration and running up and down the steps a few times to heat up before you walk in the lab. (more tricks phlebotomists have told me over the years)
I just wish they could draw from the big varicose vein in my leg... I keep offering, but they can't use it, darn!
(risk of throwing a clot is too high)
"If Americans want to live the American Dream, they should go to Denmark." - Richard Wilkinson