I have some more tips for 'difficult sticks' - like that name!
When I was a blood donor, I found if I did some extra exercise like going up and down stairs several times, it got my veins pumped up a treat. Then when I could no longer do that, I'd go somewhere private and swing my arms around like a windmill. The centrifugal effect did the same thing.
Now my sister (Janis) has always had problems in this regard. She managed to solve them by taking a hot weatbag with her and putting it on her arm for the 5-10 mins she would wait. Never has a problem now!