SQL Server: is there a way to prevent user from seeing all databases in an instance?

Is there a way to prevent that a user sees all databases in an instance? I tried to deny this from user 'mark' by

DENY VIEW ANY DATABASE TO mark

but this prevented hi开发者_StackOverflow中文版m to see (in the SSMS Object Explorer) also the database he is attached to (as a db_reader).

In this case you DENY VIEW ANY DATABASE TO public because "mark" is a member of public (as are all logins). Reference

You don't remove rights for logins indivially because then all rights are lost even where expected.

Generally, if a login has permissions on an object (database, table, whatever) they can see that object in Object Explorer in SSMS

Edit: it's not foolproof and the database owner needs changed. Sorry, forgot about that.

Even if the DB is visible, no rights are conferred or implied.