  We show that well-posed, conformally-decomposed formulations of the 3+1
Einstein equations can be obtained by densitizing the lapse and by combining
the constraints with the evolution equations. We compute the characteristics
structure and verify the constraint propagation of these new well-posed
formulations. In these formulations, the trace of the extrinsic curvature and
the determinant of the 3-metric are singled out from the rest of the dynamical
variables, but are evolved as part of the well-posed evolution system. The only
free functions are the lapse density and the shift vector. We find that there
is a 3-parameter freedom in formulating these equations in a well-posed manner,
and that part of the parameter space found consists of formulations with causal
characteristics, namely, characteristics that lie only within the lightcone. In
particular there is a 1-parameter family of systems whose characteristics are
either normal to the slicing or lie along the lightcone of the evolving metric.
