  We examine the structure of soft supersymmetry breaking terms in KKLT models
of flux compactification with low energy supersymmetry. Moduli are stabilized
by fluxes and nonperturbative dynamics while a de Sitter vacuum is obtained by
adding supersymmetry breaking anti-branes. We discuss the characteristic
pattern of mass scales in such a set-up as well as some features of 4D N=1
supergravity breakdown by anti-branes. Anomaly mediation is found to always
give an important contribution and one can easily arrange for
flavor-independent soft terms. In its most attractive realization, the modulus
mediation is comparable to the anomaly mediation, yielding a quite distinctive
sparticle spectrum. In addition, the axion component of the modulus/dilaton
superfield dynamically cancels the relative CP phase between the contributions
of anomaly and modulus mediation, thereby avoiding dangerous SUSY CP violation.
