A new family of time integration algorithms is presented for solving structural dynamics problems. The new method, denoted as the generalized-α method, possesses numerical dissipation that can be controlled by the user. In particular, it is shown that the generalized-α method achieves high-frequency dissipation while minimizing unwanted low-frequency dissipation. Comparisons are given of the generalized-α method with other numerically dissipative time integration methods; these results highlight the improved performance of the new algorithm. The new algorithm can be easily implemented into programs that already include the Newmark and Hilber-Hughes-Taylor-α time integration methods.