Now no documents needed if you limit your activities to BTC, USD.LakeBTC, and EgoPay USD.
But deposit from EgoPay is virtually impossible...

I have the same feelings

I hate EgoPay, it always makes me wait for a long time.
Sorry guys. EgoPay said they are working on it but did not provide an ETA. It's out of our control. You may want to consider other means of deposit such as bank wire and Ripple network.
Could you open a SEPA account?
I saw lakebtc recently opened a spea account, but it seems only accept SEK..
No matter what you deposit currency, sepa will help you converted into SEK.
yes, if you transfer in the EU, you can select the currency in the recipient's account. So if you have EUR, you can still send SEK, they will convert it as well.
Plus if you have a SEK account and you receive EUR, I'm also sure it gets converted right away.