 For a constructive empiricist, it would be natural to think that among empirically adequate theories one theory \(T_{2}\) is better than another theory \(T_{1}\) if \(T_{2}\) entails more true observational statements than \(T_{1}\). Such a comparison makes sense at least if the observation statements entailed by \(T_{1}\) are a proper subset of those entailed by \(T_{2}\). Kemeny and Oppenheim (1956) gave a similar condition in their definition of reduction: \(T_{1}\) is reducible to \(T_{2}\) if and only if \(T_{2}\) is at least as well systematized as \(T_{1}\) and \(T_{2}\) is observationally stronger than \(T_{1}\), i.e., all observational statements explained by \(T_{1}\) are also consequences of \(T_{2}\). Variants of such an empirical reduction relation has been given by the structuralist school in terms of set-theoretical structures (Stegmüller 1976; Scheibe 1986; Balzer et al. 1987; Moulines 2000). A similar idea, but applied to cases where the first theory \(T_{1}\) has been falsified by some observational evidence, was used by Lakatos in his definition of empirically progressive research programmes: the new superseding theory \(T_{2}\) should have corroborated excess content relative to \(T_{1}\) and \(T_{2}\) should contain all the unrefuted content of \(T_{1}\) (Lakatos and Musgrave 1970). The definition of Kuipers (2000) allows that even the new theory \(T_{2}\) is empirically refuted: \(T_{2}\) should have (in the sense of set-theoretical inclusion) more empirical successes, but fewer empirical counter-examples than \(T_{1}\). 