Deleting portions of a live trace vector

[templebolekcreative]

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.

[Monika Gause]

How did you trace it? WIth overlapping shapes? In that case you cannot delete the punches, but you need to instead select the outer shape and that punch and then make a compound path (Object > Compound path > Make)

[Myra Ferguson]

You can access the Image Trace settings that Monika mentioned where you can set Abutting which creates cutout paths (as opposed to Overlapping) by going to Window > Image Trace, twirling open Advanced, and setting the Method: