Virtualbox images under QEMU-KVM

Having installed QEMU-KVM in Ubuntu 14.04, I find it copes very well with an ISO image(or CD/DVD) and even an image created under Xen (on another machine), but not VDI images. I was under the impression that KVM could read VDI images, and that this would be included under the "Import existing disk image" option, but I just get an error -

Booting from Hard Disk
Boot failed: not a bootable disk
No bootable device

yet it was using this option that it loaded the Xen image correctly.

What am I doing wrong?