  We show that every formal embedding sending a real-analytic strongly
pseudoconvex hypersurface in $M\subset \C^N$ into another such hypersurface in
$M'\subset \C^{N+1}$ is convergent. More generally, if $M$ and $M'$ are merely
Levi-nondegenerate, the same conclusion holds for any formal embedding provided
either that the embedding is CR transversal or the target hypersurface does not
contain any complex curves.
