  Let $M$ be a smooth manifold equipped with a conformal structure, $E[w]$ the
space of densities with the the conformal weight $w$ and $D_{w,w+\de}$ the
space of differential operators from $E[w]$ to $E[w+\delta]$. Conformal
quantization $Q$ is a right inverse of the principle symbol map on
$D_{w,w+\delta}$ such that $Q$ is conformally invariant and exists for all $w$.
This is known to exists for generic values of $\delta$. We give explicit
formulae for $Q$ for all $\delta$ out of the set of critical weights. We
provide a simple description of this set and conjecture its minimality.
