  We propose a variant to the Etingof-Kazhdan construction of quantization
functors. We construct the twistor J_\Phi associated to an associator \Phi
using cohomological techniques. We then introduce a criterion ensuring that the
``left Hopf algebra'' of a quasitriangular QUE algebra is flat. We prove that
this criterion is satisfied at the universal level. This provides a
construction of quantization functors, equivalent to the Etingof-Kazhdan
construction.
