For a propositional deductive system $\text{L}$ with a disjunction $\vee$, the property that whenever $A\vee B$ is a theorem of $\text{L}$ and $\phi$ and $\psi$ have no atomic variables in common, then either $\phi$ is an $\text{L}$-theorem or $\psi$ is an $\text{L}$-theorem. Halldén completeness can be recognized as a weak form of the disjunction property.