Deleting portions of a live trace vector

When I create a vector by doing a live trace, then expand. 

With show transparent background selected I can use the direct selection tool to select the white background around the vector and delete it. However, when I select an area such as the center of a D or a P with the direct selection tool and hit back space, the center of the letter fill with whatever color the letter is rather than showing the transparent background. What am I doing wrong?  Thank you for the help.