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A detailed study of the scintillation light pulse shape in CsI(Tl) at room temperature as a function of incoming photon energy in 6-662 keV energy range is presented. Three samples of CsI(Tl) of different amount of Tl dopant (0.01, 0.06 and 0.25 mol%) were used in measurements. A delayed coincidence single photon counting method was applied to measure the decay times in the microsecond range. Three-exponential function was fitted to the time spectra to describe the light pulse shape, which resulted in three components of tau1 = 730 plusmn 30 ns (fast), tau2 = 3.2 plusmn 0.3 mus (slow) and tau3 = 16 plusmn 2 mus (tail). The intensity of the second component was found to be sensibly independent of photon energy, whereas the intensities of the first and third ones varied with the energy of absorbed photon in low energy region. For a given crystal the most intense fast component was measured for 6-keV X-rays from 55Fe at the cost of decreasing intensity of the slowest one. Furthermore, the intensity of the fast component depends on Tl concentration and reaches its maximum value for the 0.06 mol% doping, close to the well-know optimal concentration of 0.1 mol%.