How to specify a "private road"?

I think there is no tag to specify a “private road”: the decreasing levels of importance of highways are primary / secondary / tertiary / residential. But a lot of streets are private, which should be below “residential”.
“Private” would mean with restricted access, for instance with a gate at the entrance.

Would such a tag be redundant with any other?
Thanks

(and by the way, to link this discussion with a previous one about parkings with entrance and exit on distinct roads, a parking could be specified as a “private road”, the idea being that nobody would consider it as a shortcut.)

I would tag the road as:
-highway=unclassified
-access=private
And add to a node where the gate is:
-highway=gate

But this is Q&A stuff, not development → moved

I mapped one of these last week, and today I was showing off my good local knowledge about cool short cuts on bike.

And they had removed the gate, and this was one of those huge “gates of mordord” gates. So it was now ok to go by bike there…