Inspired by the so-called transmission eigenvalues, a new class of simple spectra for inverse scattering problems is introduced. These spectra can be interpreted as averaged Steklov eigenvalues. We first present the general structure of the associated eigenvalue problems, and then show how the corresponding eigenvalues can be reconstructed from multi-static data at a fixed frequency using the inside–outside duality method.The simplicity of the spectrum enables the design of an efficient, non-iterative inversion method for identifying macroscopic indicator functions in highly cluttered media. Numerical results based on synthetic data are provided to illustrate and validate the theoretical findings. Finally, we discuss possible extensions to electromagnetic problems and anisotropic media.This work is based on a collaboration with L. Audibert, M. Chavanne, and F. Pourre.