The use of an annular anti-Compton mantle of NaI(Tl) in conjunction with the following scintillation spectrometer types has been investigated: direct and total absorption gamma spectrometer, anti-Compton spectrometer, summing Compton spectrometer, pair spectrometer, coincidence spectrometer employing the pair spectrometer plus an additional detector, multiple coincidence spectrometer, ordinary and sum-peak coincidence spectrometers, sum-coincidence spectrometer and a spectrometer for the detection of gammas and gamma cascades in coincidence with positons. In these spectrometers systems, the annulus functions as the principal detector or is used for coincidence or anti-coincidence gating. Suitable electronic and geometrical arrangements, shielding, collimators and antiscattering shields are described. Most of the spectrometer combinations feature high efficiency, low background and spectra with low Compton tails. Many of the results obtained are applicable also to systems containing semiconductor radiation detectors. The advantages and limitations of the various methods are discussed and a number of further application possibilities of coincidence spectrometers employing an anti-Compton mantle are suggested.