In experiments on positronium annihilation in three photons, the background rate of triple-coincident events is usually measured by performing a separate counting run, in which one of the detectors is moved out of the three quanta annihilation plane. A thorough analysis shows that this approach can entail systematic errors and we suggest an alternative procedure. By employing a few auxiliary coincidence modules, the new approach avoids the necessity of a further dedicated counting run with modified detector geometry. Experimental results confirm the viability and accuracy of the method. ©1998 American Institute of Physics.