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The authors have constructed a 4 metre length thulium-doped ZBLAN fibre amplifier optically pumped at 0.8 μm by a tuneable Ti:Sapphire and at 1.06 μm by an Nd3+: YAG laser. The authors obtained 12.5 dB for small-signal gain at 60 mW for the two pumps' optical power. The behaviour of the amplifier has been analysed with the optical power of the signal approaching the saturation condition (-5 dBm) and at different wavelengths for the Ti: Sapphire pump laser. A model was developed for the optimisation of the amplifier for signal power below the saturation intensity at wavelengths between 1.49 and 1.53 μm (S-band). This shows an empirical quadratic dependence of the Nd3+: YAG power with respect to the Ti:sapphire power in order to obtain the maximum photon conversion efficiency making the optimised amplifier employable as a booster amplifier in the supporting telecommunication band.