EU or offshore banks allowing USD accounts?

[TheMetetron]

I'm interested in what people can find out for me. My Swedish bank wants a $25,000 minimum deposit to open one for me, and I have no need for that much money sitting in a non-interest bearing account. Trying to see if I can get something in Switzerland or elsewhere in the EU without restrictions such as this. If not, offshore European or offshore Caribbean banks are okay.

Requirements:

- Must accept US Citizens (also have Swedish residency so if that helps for an EU bank, great).
- Minimums under $10,000.
- No ridiculous fees.
- Easy access to funds through online wire transfers, debit cards (without ridiculous fees), credit cards, or other means.
- Easy deposits as well.
- Good online banking (obviously).

Anything from a major bank is preferred. If it's in the EU, I don't mind traveling there personally if need be, but online account set-up would be fantastic.

Thanks.


Edit: I'm guessing Gibraltar and Isle of Man are my best hopes.