In this document we make good on all the assertions we made in the previous paper “Moduli spaces of commutative ring spectra ”  wherein we laid out a theory a moduli spaces and problems for the existence and uniqueness of E∞-ring spectra. In that paper, we discussed the the Hopkins-Miller theorem on the Lubin-Tate or Morava spectra En; in particular, we showed how to prove that the moduli space of all E ∞ ring spectra X so that (En)∗X ∼ = (En)∗En as commutative (En) ∗ algebras had the homotopy type of BG, where G was an appropriate variant of the Morava stabilizer group. This is but one point of view on these results, and the reader should also consult , , and , among others. A point worth reiterating is that the moduli problems here begin with algebra: we have a homology theory E ∗ and a commutative ring A in E∗E comodules and we wish to discuss the homotopy type of the space T M(A) of all E∞-ring spectra so that E∗X ∼ = A. We do not, a priori, assume that T M(A) is non-empty, or even that there is a spectrum X so that E∗X ∼ = A as comodules.