© 2018 authors. Published by the American Physical Society. A recent cosmological bound on the gravitino mass, m3/2<4.7 eV, together with LHC results on the Higgs mass and direct searches, excludes minimal gauge mediation with high reheating temperatures. We discuss a minimal, vector-mediated model which incorporates the seesaw mechanism for neutrino masses, allows for thermal leptogenesis, ameliorates the μ problem, and achieves the observed Higgs mass and a gravitino as light as 1-2 eV.