The shape and intensity of backscatter peaks in pulse-height spectra have a complicated dependence on details of detector design, gamma-ray energy and geometry. In addition they show a remarkably strong systematic dependence on the atomic number of the scattering material and even manifest specifically solid state effects. The external backscatter peak can be regarded as a weighted composite of Compton profiles with an unexploited potential for revealing small changes in the electron momentum spectra of the scattering material. Its sensitivity in this role could be improved by the use of detectors with very thick depletion layers and by a redesign of the coldfinger to diminish the internal backscatter peak. By reduction of the source energy and the use of a small absorber post, the system evolves into a new type of Compton-profile spectrometer of outstanding efficiency and small dimensions.