Did you know KVM has a way to enable discard pass thru? I did, but then I forgot and had to google again.

This is how you do it:

kvm -drive discard=unmap,file=debian.qcow2,id=ff,if=none \
    -device virtio-scsi-pci -device scsi-disk,drive=ff

When booted, you have to make sure your fs is mounted with discard option, and can then do:

fstrim /

And the image on the host should be significantly smaller. Use du or ls -alsh, not just ls, because ls does not display actual disk usage if you don't pass -s:

1,4G -rw-r--r--  1 root root 4,0G apr  7 17:22 debian.img

Now you know.

Did you know you can start kvm with vnc disabled and then attach it in monitor? And change CD or save vm snapshot?