We discuss singlet extensions of the MSSM with $Z_4^R$ 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.