  We present quasi-Banach spaces which are isomorphic to the duals of
combinatorial Banach spaces and which are equipped with quasi-norms that seem
to be much easier to handle than the original dual norms. In particular we show
nice quasi-renormings of the dual Schreier spaces. We use it to show that the
duals to the combinatorial Banach spaces induced by large families (in the
sense of Lopez-Abad and Todorcevic) are $\ell_1$-saturated and do not have the
Schur property.
