The preprint: On Branched Covers in Topos Theory is available from my home page http://www.math.ubc.ca/~funk/ in postscript or .dvi format. This is a revision and extension of a preprint I had posted from Cyprus in June, 98. Abstract: We present some new findings concerning branched covers in topos theory. Our discussion involves a particular subtopos of a given topos that can be described as the smallest subtopos closed under small coproducts in the including topos. Our main result is a description of the covers of this subtopos as a category of fractions of branched covers, in the sense of R. Fox, of the including topos. We also have some new results concerning the general theory of KZ-doctrines, such as the closure under composition of discrete fibrations for a KZ-doctrine, in the sense of Bunge-Funk.