Deallocate some extents on encrypted root device in order to increase free physvolume
 

I just install Debian 8.1. I allocated for lvm volume group almost all disk (300 GiB ) to encrypted partition and a little bit for boot. I want to make smaller 50GiB encrypted physical volume and install different xen OS to the free space.

Is it possible to do it without data loss? How?

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System info:
/dev/dm-1 ext4 /
/dev/sda1 ext2 /boot

Files in /dev/mapper :
control
hostname--vg-root
hostname--vg-swap_1
sda5_crypt

I think I used this Ubuntu how-to when I wanted to test this recently.
I think I used gparted to do the partition resizing rather than fdisk. I did this on a system I could afford to lose, but everything went fine.