I find this whole thing annoying. They are making it almost impossible to use self signed certificates. Sometimes that is all that is needed, especially for an in-house app. A non SSL site is irrelevant if you are not entering data. Once all of the bad guys are on SSL, the situation becomes worse than what we had.
Yandex says it more formally, though still some people might understand it, that there is nothing wrong with the site. Banking sites are green, SSL protected are colored normally.