A new design for a $\gamma$-ray Compton scattering spectrometer is presented. The spectrometer uses an annular geometry that is the inversion of the annular geometry used in earlier experiments with americium $\gamma$-rays. A small source is placed directly in front of the detector so that it is the detector and not the source that provides the annulus. Measurements of the Compton profile of aluminium are used to evaluate the new design. For small samples it is possible to increase the intensity by a factor of up to 10$^4$ while maintaining the resolution. This should make it possible to obtain accurate data for many compounds that could not previously be studied because of the difficulties associated with obtaining large single crystals.