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Let $\Omega$ be a bounded strictly pseudoconvex domain in $C^2$ with asmooth, connected and compact boundary M and having a CR structure $J_0$induced from $C^2$. Assume this CR structure has zero Webster torsion. Then ifwe deform the CR structure through real-analytic dependence on the deformationparameter and such that each deformed structure along the deformation path issmooth and embeddable in $C^2$, we show that for small deformations of the CRstructure $J$ from $J_0$, the associated CR Paneitz operator for $J$ isnon-negative. We also show that the Webster curvature for any ellipsoid in$C^2$ is positive. The results in this paper complement and provide partialconverses to our earlier paper, (to appear Duke Math. J.) arxiv: 1007.5020.

Embedded Three Dimensional CR Manifolds and the Non-Negativity of Paneitz Operators