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We discuss the possibilities for the direct detection of neutralino darkmatter via elastic scattering in variants of the minimal supersymmetricextension of the Standard Model (MSSM) with non-universalsupersymmetry-breaking contributions to the Higgs masses, which may be eitherequal (NUHM1) or independent (NUHM2). We compare the ranges found in the NUHM1and NUHM2 with that found in the MSSM with universal supersymmetry-breakingcontributions to all scalar masses, the CMSSM. We find that both the NUHM1 andNUHM2 offer the possibility of larger spin-independent dark matter scatteringcross sections than in the CMSSM for larger neutralino masses, since they allowthe density of heavier neutralinos with large Higgsino components to fallwithin the allowed range by astrophysics. The NUHM1 and NUHM2 also offer morepossibilities than the CMSSM for small cross sections for lower neutralinomasses, since they may be suppressed by scalar and pseudoscalar Higgs massesthat are larger than in the CMSSM.

Update on the Direct Detection of Dark Matter in MSSM Models with Non-Universal Higgs Masses