One of the better studied properties for operators in judgment aggregation is independence, which essentially dictates that the collective judgment on one issue should not depend on the individual judgments given on some other issue(s) in the same agenda. Independence is a desirable property for various reasons, but unfortunately it is too strong, as, together with mild additional conditions, it implies dictatorship. We propose here a weakening of independence, named agenda separability and show that this property is discriminant, i.e., some judgment aggregation rules satisfy it, others do not.