Proc. Amer. Math. Soc. 143 (2015), no. 6, 2597–2612. Also available on the arXiv.We study a family of transcendental entire functions of genus zero, for which all of the zeros lie within a closed sector strictly smaller than a half-plane. In general these functions lie outside the Eremenko-Lyubich class. We show that for functions in this family the fast escaping set has Hausdorff dimension equal to two.