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A rate equation approach is used to model an experimentally realized ~ 2 mum Tm3+-doped tellurite fiber laser utilizing an in-band pumping scheme (3H6 rarr 3F4) . Excellent agreement between the theoretically predicted and experimentally measured slope efficiency is obtained. It is shown that in order to achieve agreement between the predicted and measured thresholds it is important to include cross-relaxation mechanisms with the 3H4 level, even with the in-band pumping scheme. By fitting the results of the model with level lifetime measurements and the threshold pump powers we have extracted the cross-relaxation parameters of Tm-doped tellurite glass.