In 1987 McMullen proved that the Hausdorff dimension of the Julia set of complex exponentials is equal to 2. This result has been extended by Baranski and Schubert to all entire functions of finite order in the Eremenko-Lyubich class B. The purpose of this talk is to present a result on the Hausdorff dimension of the Julia set for entire functions which do not belong to the class B. We show that if the growth of the function f is sufficiently regular then the Julia set and the escaping set of f have Hausdorff dimension 2. This is a joint work with W.Bergweiler.