Accurate jump relations for Chapman-Jouguet (CJ) and overdriven gaseous detonation waves are derived. The difficulty in accurately approximating the energy equation in a perfect gas two-gamma detonation jump formulation is resolved by adjusting the authentic combustion heat release in terms of linearly approximated up- and down-stream sensible enthalpies at the CJ condition where it is exactly satisfied for CJ and well approximated for overdriven waves. The basis of the success of the derived two-gamma jump relations is explained. Explicit thermodynamic jump relations across a normal detonation wave are obtained. These approximate-jump relations depend on the following four parameters: gamma(J), upstream isentropic exponent (or the gamma giving pertinent upstream sound speed for defining M-1); gamma(J), CJ isentropic exponent (or the gamma giving pertinent sound speed for a CJ state); M-1, upstream Mach number; and M-J, CJ Mach number, gamma(j) and M-J can be obtained numerically, or experimentally with the derived jump relations. Comparisons of exact numerical and the present approximate calculation for jump conditions of CJ and overdriven detonations for methane- and hydrogen- oxygen systems show excellent agreement over a wide range of upstream Mach number, temperature, pressure, and mixture conditions.