We introduce a new family of Godunov-type semi-discrete central schemes for multidimensional Hamilton-Jacobi equations. These schemes are a less dissipative generalization of the central-upwind schemes that have been recently proposed in [Kurganov, Noelle and Petrova, SIAM J. Sci. Comput., 23 (2001), pp. 707-740]. We provide the details of the new family of methods in one, two and three space dimensions, and then verify their expected low-dissipative property in a variety of examples.