LVM doesn't work correctly

Hi Fellows,
in my machine there are two 20G HDDs and one 80G. The 80G one is reserved for media and that’s no problem. As my documents which I want to place in my Home folder are bigger than 20G, I decided to use the LVM installation.
So I selected the 80M /boot partition, created an LVM on the two 20G HDDs w/ one 7G for / and the remaining 33G for /home. Installation went fine (I selected Xfce as the hardware is not the newest).
Now I wanted to copy my personal files… and it stopped with “No space on disk left” … I checked it and in my home folder there are only 3G instead of 33.
What went wrong? I used the default settings whereever possible and tried to mess up as little as possible w/ custom settings. (Actually, the only custom setting is my background image…)
Any Idea?