Cloning databases using rsync

I regularly copy all my postgresql data onto another computer and access
it locally there. This works if I use pg_dump, transfer the output
file, and feed that file into psql. However, I would prefer to copy
the databases using rsync instead of pg_dump, because it's simpler and
faster. (I know the server has to be down to avoid corruption.)

rsync -avx --delete 132.205.86.95:/var/lib/postgresql /var/lib

After doing this, when I run psql I get

psql: FATAL: database "xxxxx", OID 12345, has disappeared from
pg_database

where "xxxxx" and 12345 depend on the database. /var/lib/postgresql is
identical on both systems, and so is /etc/postgresql other than
host-specific things like IP addresses. The version is the same (8.0).
The directory "12345" exists. Any ideas of what else might have to be
copied?

David