  We study the implications of a large baryogenesis temperature, $T_B =
O(10^{10}$ GeV), on the mass spectrum of superparticles in supersymmetric
extensions of the standard model. Models with a neutralino as lightest
superparticle (LSP) are excluded. A consistent picture is obtained with the
gravitino as LSP, followed by a higgsino-like neutralino (NSP). Gravitinos with
masses from 10 to 100 GeV may be the dominant component of dark matter.
