In this paper, we propose a variant of stable model semantics fordisjunctive logic programming and deductive databases. Thesemantics, called minimal founded, generalizesstable model semantics for normal (i.e. non-disjunctive) programs,but differs from disjunctive stable model semantics (the extensionof stable model semantics for disjunctive programs). Compared withdisjunctive stable model semantics, minimal founded semantics seemsto be more intuitive, it gives meaning to programs which aremeaningless under stable model semantics and is no harder tocompute. More specifically, minimal founded semantics differs fromstable model semantics only for disjunctive programs havingconstraint rules or rules working as constraints. We study theexpressive power of the semantics, and show that for generaldisjunctive datalog programs it has the same power as disjunctivestable model semantics.