The Triplet extension of the MSSM (TMSSM) alleviates the little hierarchy problem and can provide SM-like Higgs signatures even in the presence of a rather light CP-odd Higgs. It is also compatible with enhancements in the gamma+gamma and gamma+Z decays of the CP-even Higgs. In this talk we review these issues. In particular we quantify the above loop-induced enhancements, and we determine how they are reduced once the lightest neutralino is assumed to be the dark matter particle.