We report two novel determinations of |Vub| with reduced model dependence, based on measurements of the mass distribution of the hadronic system in semileptonic B decays. Events are selected by fully reconstructing the decay of one B meson and identifying a charged lepton from the decay of the other B meson from Υ(4S)→BB̄ events. In one approach, we combine the inclusive B̄→Xuν̄ rate, integrated up to a maximum hadronic mass mX<1.67GeV/c2, with a measurement of the inclusive B→Xsγ photon energy spectrum. We obtain |Vub|=(4.43±0.38stat±0.25syst±0.29theo)×10-3. In another approach we measure the total B̄→Xuν̄ rate over the full phase space and find |Vub|=(3.84±0.70stat±0.30syst±0.10theo)×10-3. © 2006 The American Physical Society.