Giraud_Elementary_?

Hi, in this posting I will use the terminology used by most people in the list. There are Grothendieck, Giraud and Elementary (Lawvere-Tierney) topos. Grothendieck are Giraud and Elementary, my question is: Are Elementary Giraud topos which are not Grothendieck ? Examples ? greetings e.d. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]