How to resize a LVM partition?

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http://askubuntu.com – I want to shrink my second (lvm) partition, so I can create a new partition in the freespace. I am using Live-CD to do so, because I know I can't resize/move this partition while it is in use. When I opened GParted in Live-CD, I realized that I could not resize the partition, because when I right-click it, the option "resize/move" is disabled. I tried to unmount it, to "lazy" unmount it (umount -l /dev/sda2) but it didn't work. A screenshot from GParted: (HowTos)