Singlet extensions of the MSSM with Z_4^R symmetry

We discuss singlet extensions of the MSSM with $\mathbb{Z}{4}^R$ symmetry. We show that holomorphic zeros can avoid a potentially large coefficient of the term linear in the singlet. The emerging model has both an effective mu term and a supersymmetric mass term for the singlet mu_N which are controlled by the gravitino mass. The mu term turns out to be suppressed against mu_N by about one or two orders of magnitude. We argue that this class of models might provide us with a solution to the little hierarchy problem of the MSSM.