  The Higgs mass implies fine-tuning for minimal theories of weak scale
supersymmetry (SUSY). Non-decoupling effects can boost the Higgs mass when new
states interact with the Higgs, but new sources of SUSY breaking that accompany
such extensions threaten naturalness. We show that two singlets with a Dirac
mass can increase the Higgs mass while maintaining naturalness in the presence
of large SUSY breaking in the singlet sector. We explore the modified Higgs
phenomenology of this scenario, which we call the "Dirac NMSSM."
