For CsI single-crystal excitation spectra of fast intrinsic luminescence (FIL) peaking at 300 nm at 300 K, self-trapped exciton luminescence (280 and 340 nm) and impurity-induced emission (450 nm) have been measured in the VUV (20-130 eV) and X-ray (near L 3 edge of iodine) energy regions. FIL excitation spectra were substantially different from those of other bands. FIL yield increases by a factor of more than 10 with the increase of the excitation energy from 20 to 50 eV, it also increases at L 3 edge of iodine. These regions are characterised by the increase of local density of secondary electronic excitations. We suggest that the relaxation of an exciton into FIL generating state occurs only in the region of the crystal perturbed by another electronic excitation or defect.