  The aim of this paper is to extend the method of improving cloaking
structures in the conductivity to scattering problems. We construct very
effective near-cloaking structures for the scattering problem at a fixed
frequency. These new structures are, before using the transformation optics,
layered structures and are designed so that their first scattering coefficients
vanish. Inside the cloaking region, any target has near-zero scattering cross
section for a band of frequencies. We analytically show that our new
construction significantly enhances the cloaking effect for the Helmholtz
equation.
