Who makes this bra??

[Triskeliongirl]

While this bra also does not meet all of your criteria it meets many, and I like it a lot: http://www.teamestrogen.com/prodMC_350006.html

Its the moving comfort cara bra. While it does have an underwire and does not have any padding, the wire is very comfortable, and the bra itself is extremely comfortable. I like that its flattering, not flattening (it works by encapsulation not compression), it does have a normal back closure, wide straps, and could even be worn everyday (i.e. not for sports only). Even with the wire it has a thick elastic band under the wire, and I secure my HRM strap under that and it works and feels great. I really don't feel the wire (but I am a C cup, so maybe I just appreciate more the extra support).

The cups are very thin, which increases breathability, but I will warn you that nipple show through can be an issue depending on how close fitting your shirt is. Also, while supportive enough for cycling, I would not recommend it for truly high impact sports like running.