  We present a new formulation for N=1, D=10 supergravity in superspace, in
presence of a Lorentz Chern-Simons-form. This formulation entails the following
properties: it furnishes a solution of the Bianchi identities that is
algebraically consistent to all orders in alpha'; at first order it is the
simplest formulation proposed so far, and it is therefore most suitable for an
explicit higher order analysis; it allows a well defined perturbative expansion
in alpha', in which no poltergeist fields appear; it reconciles the two
different classes of first order solutions available in the literature, that
until now appeared physically inequivalent.
