The present disclosure relates generally to a layered structure for a radome for use with radiation of a free space frequency. The present disclosure relates more particularly to a layer structure for a radome having a core with an inside surface and an exposed outside surface. The core includes a first core layer having a first relative permittivity of at least 2.3 and a second core layer having a second relative permittivity of at least 2.3. The first core layer is no more than 0.75 mm from the outside surface of the core. An inner structure is disposed on the inside surface of the core and has at least one layer. Each of the first relative permittivity and second relative permittivity is at least 0.4 greater (e.g., at least 0.7 greater, at least 1 greater, or at least 1.3 greater) than a relative permittivity of any layer in the inner structure.