  We show that if $2k\geq n$, then a k-connected weak n-category $A$ can be
``delooped'' to a k+1-connected weak n+1-category $Y$ with $Hom_Y(y,y)\cong A$.
This is the essential part of the ``stabilization hypothesis'' of Baez and
Dolan q-alg/9503002, math/9802029.
