  We consider singular integrals associated to a classical Calder\'on-Zygmund
kernel $K$ and a hypersurface given by the graph of $\varphi(\psi(t))$ where
$\varphi$ is an arbitrary $C^1$ function and $\psi$ is a smooth convex function
of finite type. We give a characterization of those Calder\'on-Zygmund kernels
$K$ and convex functions $\psi$ so that the associated singular integral
operator is bounded on $L^2$ for all $C^1$ functions $\varphi$.
