  Both electroweak precision measurements and simple supersymmetric extensions
of the standard model prefer a mass of the Higgs boson less than the
experimental lower limit of 114 GeV. We show that supersymmetric models with R
parity violation and baryon number violation have a significant range of
parameter space in which the Higgs dominantly decays to six jets. These decays
are much more weakly constrained by current LEP analyses and would allow for a
Higgs mass near that of the $Z$. In general, lighter scalar quark and other
superpartner masses are allowed and the fine-tuning typically required to
generate the measured scale of electroweak symmetry breaking is ameliorated.
The Higgs would potentially be discovered at hadron colliders via the
appearance of new displaced vertices. The lightest neutralino could be
discovered by a scan of vertex-less events LEP I data.
