Posts/pages not public, but available to Subscriber users?

Hello,

I need to create pages / posts, that are not public to anyone on the web (probably just coming to the website by mistake), but available to Subscriber-level users of the web.

I know about the existing Private post feature, but it makes the page visible only for editors and admins, and all other users (with lower premissions) cannot see them. But I cannot give some of my users such high privileges. And I need to specify which content is really public to anyone, and whis is only for resgistered users.

Is it possible?

Thx, Honza