  Recently, an extension of the standard model based on ideas of Lee and Wick
has been discussed. This theory is free of quadratic divergences and hence has
a Higgs mass that is stable against radiative corrections. Here, we address the
question of whether or not it is possible to couple very heavy particles, with
masses much greater than the weak scale, to the Lee-Wick standard model degrees
of freedom and still preserve the stability of the weak scale. We show that in
the LW-standard model the familiar see-saw mechanism for generating neutrino
masses preserves the solution to the hierarchy puzzle provided by the higher
derivative terms. The very heavy right handed neutrinos do not destabilize the
Higgs mass. We give an example of new heavy degrees of freedom that would
destabilize the hierarchy, and discuss a general mechanism for coupling other
heavy degrees of freedom to the Higgs doublet while preserving the hierarchy.
