Effective epimorphisms and pretopologies

Hi all, An effective epimorphism is a map which is the quotient of its kernel pair. I would like to use the term 'effective pretopology' to denote a Grothendieck pretopology such that all the covers have the additional property that they are effective epimorphisms (I'm assuming the covering families consist of single maps). Has this been done before? This seems to conflict a little with the notion of effective topology as defined by Mike Barr in 'On categories with effective unions'. There the notion of topology is an endomorphism of the subobject functor. But perhaps someone can enlighten me on this. David Roberts