I'm also a 36DD and very happy with my Moving Comfort Fiona bra, and use it for hiking, jogging, road and mountain biking. I could even jump rope in this sucker. I was worried about the adjustable straps on my misshapen collarbone but they aren't rubbing on that or on the normal side, either. So far everything's staying in place. They do seem to be sized a hair bigger than my regular bras so I got the 36D. I've only had it for a month but use it about 3 times a week-so far it's holding up fine under the washings/bouncings.
I used to have an open mind but my brains kept falling out.