I know you said you have been measured and are wearing the correct size, but your post makes me think that you are wearing a band that is too big. You should be getting enough support from your band that your straps are basically unnecessary, and your breasts should not be weighing you down. The correct bra will give you the lift you want without being a push-up.
I wear a 36FF (or a US size 36H) so I know what you are talking about, and I know that I had been measured multiple times as a 38 or even 40 DD before I found the right bras. The difference is amazing. My favorite brands are Panache, Freya, Fantasie and Elomi. All are made in the UK (I think) and they seem to have a whole different philosophy about bras there. They cut way more sizes, and don't expect everyone to fit into A, B, C, D or DD.
You can size yourself at home, here is a link to my favorite place to buy bras. They have some great info on sizing and instructions for you to do it yourself. Most places that size women will take your measurement around your ribcage and then add a certain number of inches to the measurement. This is crazy. If you measure 30" around the ribs, you are a size 30, not a 34 or 36. Give it a try and see if you still get a 34DD as your size, can't hurt, might help.
http://www.breakoutbras.com/sizing