The problem of obtaining BaF2 crystals with a predominant sub-nanosecond luminescence component has been considered. A detailed analysis of methods for suppressing the slow component of the crystal luminescence was carried out. It was shown that the introduction of a number of dopants led to the suppression of the slow component, but, as a rule, the intensity of the sub-nanosecond component decreased, and the transparency and radiation hardness of the crystal also deteriorated. The results of spectral and kinetic measurements of BaF2:Tm and BaF2:Sc luminescence were presented. It was shown that the solution of the problem can be achieved by using an undoped BaF2 crystal in combination with a filter suppressing the slow luminescence component.