  We introduce a class of embedded CR manifolds satisfying a geometric
condition that we call weak $Y(q)$. For such manifolds, we show that dbar-b has
closed range on $L^2$ and that the complex Green operator is continuous on
$L^2$. Our methods involves building a weighted norm from a microlocal
decomposition. We also prove that at any Sobolev level there is a weight such
that the complex Green operator inverting the weighted Kohn Laplacian is
continuous. Thus, we can solve the dbar-b equation in $C^\infty$.
