Solving the mu problem with a heavy Higgs boson

We discuss the generation of the mu-term in a class of supersymmetric models characterized by a low energy effective superpotential containing a term lambda SH1H2 with a large coupling lambda similar to 2. These models generically predict a lightest Higgs boson well above the LEP limit of 114 GeV and have been shown to be compatible with the unification of gauge couplings. Here we discuss a specific example where the superpotential has no dimensionful parameters and we point out the relation between the generated mu-term and the mass of the lightest Higgs boson. We discuss the fine-tuning of the model and we find that the generation of a phenomenologically viable mu-term fits very well with a heavy lightest Higgs boson and a low degree of fine-tuning.