[en] A mathematical model of the liquid scintillation counting (LSC) process (Malcolm and Stanley. Int. J. Appl. Rad. Isot.; 27:493 (1976)) has indicated several ways in which considerable amounts of light are normally lost from the counting process. These light losses, some of which are unexpectedly large, depend substantially upon the cylindrical symmetry of the normal counting vial. The source and relative importance of these losses are discussed, and a spherically symmetrical LSC system of much greater optical efficiency is proposed. A detailed mathematical model of the spherical system is given, and this indicates that, when using currently available photomultipliers, one might reasonably expect a counting efficiency of about 85% for an unquenched tritium sample. (author)