Sheaf of sites?

If (C,J) is a site, and F is a sheaf of sites on (C,J), in the sense that F(X) is a site for each object X of C and F(f) is a morphism of sites for each arrow f of C, are there any straightforward, useful conditions under which F forms an internal site in Sh(C,J), or is it usually necessary to construct the powerobject and work from the definition? Thanks, Barney. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]