  Motivated by the KKLT string compactification involving a
supersymmetry-breaking uplifting potential, we examine 4D effective
supergravity with a generic form of uplifting potential, focusing on the
possibility that the resulting mixed modulus-anomaly mediated soft terms
realize the little hierarchy between the Higgs boson masses $m_H$ and the
sparticle masses $m_{SUSY}$. It is noted that for some type of uplifting
potential, the anomaly-mediated contribution to $m_H^2$ at $M_{GUT}$ can cancel
the subsequent renormalization group evolution of $m_H^2$ down to TeV scale,
thereby the model can naturally realize the little hierarchy $m_H^2\sim
m_{SUSY}^2/8\pi^2$ which is desirable for the lightest Higgs boson mass to
satisfy the experimental bound. In such models, the other Higgs mass parameters
$\mu$ and $B$ can have the desirable size $\mu \sim B \sim m_H$ without severe
fine-tuning of parameters, although the gravitino is much heavier than the
Higgs boson. Those models for the little hierarchy avoid naturally the
dangerous SUSY flavor and CP violations, and predict nearly degenerate low
energy gaugino masses, pure Higgsino LSP, and also a specific relation between
the stop and gaugino masses.
