I'm familiar with the L2000, it was I who suggested one to Kavo

. To my ears, at least, it doesn't have the capacity to sound the same as a Jazz or a P, the MFD pickups are very, very different, even with coil splitting engaged, plus you can't blend the pickups like you can with a Jazz, there's a wealth of subtle changes you can make on the J.
Don't get me wrong, it's a great bass, as I've already said, but if you've got a P, you need a J. It's the law
