Chris DBlood draws have always been a horror for my son (now 6). He inherited my rolling veins. A couple of things have worked for us.
1) I always try to write down the name of the person who did the draw. If they are good, I will request them the next time. When we have found someone especially good I have gone so far as to call in on a Monday and explain that I would like to bring my son in on a day that so-and-so is working. They typically won’t give out anyone’s work schedule but I can usually get them to tell me if "I should have luck coming in on Tuesday morning" - for example.
2) When we check in for the draw (registration if in the hospital). I explain that my son has been a hard draw and ask for the absolute best person they have. I figure at a minimum they won’t give us a brand new one. Also, when whomever was "chosen" hears they are "the best" the are very motivated to have a successful one-stick draw.
3) When we meet the person drawing I am sure to mention either (1) they drew so well last time we requested them specifically, or (2) they said you are the BEST. Again this is great motivation. No one wants to fail after all that build-up.
Whenever I have been too preoccupied or busy to go through these ridiculously necessary steps we have had a horrible experience of multiple pokes, bruises and a very hysterical child.
It is a pain, but it does seem to help. (so does Elemax or Emla!)