The T3 lighted cover is very minimal. Either the original or the lighted cover basically includes the attached back cover with a front flap. It's different from a typical ereader cover like what I have for my Kobo or Tolino.
I know most people here hate goodereader but this video by them does show clearly how the Sony cover attaches.
https://www.youtube.com/watch?v=HP0TLQ1XYAI
Of the four ereaders listed in my user info to the left, the PRS-T3 with lighted cover takes up the least amount of space if I'm putting it in a pocket of my handbag. It's very slim.