A bank account for non-resident, still possible?

Hello,

From the previous posts on this forum, I have understood that it has become almost impossible to open an account in any Swiss bank unless you have large amount to deposit. Is it true, or is there still any possibility to open an account with a few thousand Euros?

If its not possible in Switzerland, are there any banks in Liechtenstein or any other place which allow that. Is it possible to do complete process online without visiting the bank?

Thanks.