Supersymmetry without a light Higgs boson but with a light pseudoscalar

We consider the lambda-SUSY model, a version of the NMSSM with large lambda H_1 H_2 S coupling, relaxing the approximation of large singlet mass and negligible mixing of the scalar singlet with the scalar doublets. We show that there are regions of the parameter space in which the lightest pseudoscalar can be relatively light, with unusual consequences on the decay pattern of the CP-even Higgs bosons and thus on the LHC phenomenology.