Can SVN only branch and tag at the highest project level?

It seems like in SVN there must be separate repository folders for
tags, branches and trunk below each project.
To me this implies that svn is only able to do these operations at the
very top of a project tree, is that really so?
I am coming from CVS(NT) and it was always possible to do the tagging
and branching for *anything* inside a project tree. For example a
subtree could be branced and tagged independently from the main
project.
Is this not possible in SVN?
If so, how can I convert my CVS repository to SVN correctly, while
preserving these properties?
We have used this on many places, for example branching out only a
single file or two in a directory while leaving the other files on
TRUNK.
Then at a later time when all is checked we merged the changes back
into TRUNK.
Is this not possible in svn?

-- 
Bo Berglund
Developer in Sweden