Summary: We discuss improved likelihood ratio tests for both the parameters in the systematic component and the dispersion parameter in the class of dispersion models [\textit{B. Jørgensen}, REBRAPE 1, No. 1, 59-90 (1987; Zbl 0715.62137)]. General formulae for the expected likelihood ratio statistic are obtained explicitly in dispersion models, which generalize previous results by \textit{G. M. Cordeiro} [J. R. Stat. Soc., Ser. B 45, 404-413 (1983; Zbl 0529.62024); Lecture Notes Stat. 32, 27-34 (1985; Zbl 0586.62108); Biometrika 74, 265-274 (1987; Zbl 0649.62024)] and \textit{G. M. Cordeiro} and \textit{G. A. Paula} [Biometrika 76, No. 1, 93-100 (1989; Zbl 0663.62068)]. The practical use of the formulae is that we can derive closed-form Bartlett corrections for these models when the information matrix has a closed-form. Various Bartlett corrections are given for special models. The formulae have advantages for numerical purposes because they require only simple operations on matrices. Algebraically, they may be handled within computer systems such as REDUCE. Some numerical examples involving real data clarify the use of these formulae.