The \(\overline \partial_b \)- Neumann problem is studied for domains \(\Omega \) contained in a strictly pseudoconvex manifold \(M^{2n+1}\) whose boundaries are noncharacteristic and have defining functions depending solely on the real and imaginary parts of a single CR function. If the Kohn Laplacian has closed range in \(L^2,\) sharp regularity and estimates for solutions are proved. The author also gives a sufficient condition on the boundary \(\partial \Omega\) for \(\square_b\) to be Fredholm on \(L^2_{(0,q)}(\Omega )\) and shows that this condition always holds when \(M\) is embedded as a hypersurface in \(\mathbb{C}^{n+1}.\) In the appendix the author proves useful general functional analytic results about elliptic regularization, which are used before.