With some TLDs e.g. .au, it is not possible to implement domain privacy.
I can't comment on .is (it may be worth investigating) but with .au domains when there was a domain transfer issue that saw registrant address info not included with the domain, the registry advised that it wasn't a problem as there is no rule stating that whois information has to be accurate.
As long as the email address gets mail to you (you could set up one especially for the domain registration) then you may be OK to enter slightly obfuscated address info. You live in Main St? Change it to Mane St. Change the house number. etc.
In all my years as a domain reseller I have never heard of postal address info ever being used for anything apart from spam. Perhaps the .au registry knows this and it is why they don't care so much about accuracy.