Secure deleting files within an encrypted disc image

I have a question about OSX 10.4.11 and secure deleting. My understanding is that even after secure delete has been used to erase a particular file, older fragments of that same file can remain on the hard drive. Assuming this also applies to secure deleting files from a mounted encrypted disc image (created using the disc utility), would I be correct in saying that even if file fragments remained, once the image is unmounted, those file fragments would be encrypted like everything else within the disc image. I guess what I'm really asking is whether, when one deletes a file from an encrypted disc image, that file data is moved outside of the encrypted data blocks into clean drive space. I don't see why this would be the case but was wondering whether anyone knew.

I appreciate one can always use the free space eraser within disc utility to "mop up" but I'm still interested about individual file deleting.

(Btw, this is my first post and as a courtesy, I did search the forums for this topic but didn't find anything. If I missed something in my search and this has already been answered, apologies!)