I tried to do this without success. AFAIK, I should be using wp_get_archives:
First, show the category:
And then, show the post title only of all the posts inside that category, newer ones on top:
-- :: I trashed my Ferrari
-- :: I won a Ferrari!
Of course, I won't have just one category, so this gets harder to do.
If this helps, my permalinks are by /postid/ and then by /posttitle/.
I had seen in the codex the get_archive stuff and it features an example with a dropdown box, so that should be a nice solution when I'll have more than 20 posts in a category.