Another tip; you can avoid excessive wait and hassle by creating a batch file to import the keys, disabling the automatic rescan that can lock the client for 10 minutes, with lines like:
C:\Program Files (x86)\Bitcoin\daemon\bitcoind importprivkey L3GMeSqH3HTcqLBsYtQtJQhLQ2iaFMq8FBHga9gek2hGXMQbskjY multibit1 false
C:\Program Files (x86)\Bitcoin\daemon\bitcoind importprivkey KxFFdK2xG9kJDXC5yQ3Ck6SFodsR1y97bNBz9tNu5uzkxzMchiG1 multibit2 false
the false disables the rescan, you can have false until the last line so only the last import makes a rescan of all addresses.
So I can use this "new" compressed private key on any client without any decompressing/converting to the old format or things like that?
A compressed address/private key combination cannot be "decompressed" for any useful purpose; a decompressed private key (which only has a flag indicating that the public key is uncompressed) has a different bitcoin address.
Some clients, notably Electrum, do not support compressed addresses (which may result in you paying more fees than you need to).