In this paper, the design of superconducting-nanowire single-photon detectors which are insensitive to the polarization of the incident light is investigated. By using high-refractive-index dielectrics, the index mismatch between the nanowire and the surrounding media is reduced. This enhances the absorption of light with electric field vector perpendicular to the nanowire segments, which is generally hindered in these kind of detectors. Building on this principle and focusing on NbTiN nanowire devices, we present several easy-to-realize cavity architectures which allow high absorption efficiency (in excess of 90%) and polarization insensitivity simultaneously. Designs based on ultranarrow nanowires, for which the polarization sensitivity is much more marked, are also presented. Finally, we briefly discuss the specific advantages of this approach in the case of WSi or MoSi nanowires.@en