Recent data from CoGeNT and DAMA are roughly consistent with a very light dark matter particle with $msim 4-10gev$ and spin-independent cross section of order $sigma_{SI} sim (1-3)times 10^{-4}pb$. An important question is whether these observations are compatible with supersymmetric models obeying $Omega h^2sim 0.11$ without violating existing collider constraints and precision measurements. In this talk, I review the fact the the Minimal Supersymmetric Model allows insufficient flexibility to achieve such compatibility, basically because of the highly constrained nature of the MSSM Higgs sector in relation to LEP limits on Higgs bosons. I then outline the manner in which the more flexible Higgs sectors of the Next-to-Minimal Supersymmetric Model and an Extended Next-to-Minimal Supersymmetric Model allow large $sigma_{SI}$ and $Omega h^2sim 0.11$ at low LSP mass without violating LEP, Tevatron, BaBar and other experimental limits. The relationship of the required Higgs sectors to the NMSSM ideal-Higgs scenarios is discussed.
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