This paper presents a new family of unconditionally stable one-step methods for the direct integration of equations of structural dynamics, which possess improved algorithmic damping properties that can be continuously controlled. The methods are compared with members of the Newmark family, the Houbolt method, and the Wilson method. The new methods are shown to have improved characteristics in terms of algorithmic damping and relative period error compared to the Wilson and Houbolt methods. The new family of algorithms is defined by a three-parameter family of algorithms, which includes the Newmark family. A new form of dissipation, called α-dissipation, is introduced by way of these algorithms. The new one-parameter family of methods is a subclass contained in the three-parameter family. The new methods involve commensurate storage when compared with the Newmark and Wilson methods, and are no more difficult to implement. The paper also discusses the spectral radius, damping ratios, and relative period error of the new methods and compares them with those of the Newmark, Houbolt, and Wilson methods. The results show that the new methods have improved characteristics in terms of algorithmic damping and relative period error compared to the Wilson and Houbolt methods. The new methods are shown to be more accurate in the lower modes than the Wilson method, yet more strongly dissipative in the higher modes. The paper concludes that the new family of algorithms is a significant improvement over the existing methods in terms of algorithmic damping and numerical dissipation.This paper presents a new family of unconditionally stable one-step methods for the direct integration of equations of structural dynamics, which possess improved algorithmic damping properties that can be continuously controlled. The methods are compared with members of the Newmark family, the Houbolt method, and the Wilson method. The new methods are shown to have improved characteristics in terms of algorithmic damping and relative period error compared to the Wilson and Houbolt methods. The new family of algorithms is defined by a three-parameter family of algorithms, which includes the Newmark family. A new form of dissipation, called α-dissipation, is introduced by way of these algorithms. The new one-parameter family of methods is a subclass contained in the three-parameter family. The new methods involve commensurate storage when compared with the Newmark and Wilson methods, and are no more difficult to implement. The paper also discusses the spectral radius, damping ratios, and relative period error of the new methods and compares them with those of the Newmark, Houbolt, and Wilson methods. The results show that the new methods have improved characteristics in terms of algorithmic damping and relative period error compared to the Wilson and Houbolt methods. The new methods are shown to be more accurate in the lower modes than the Wilson method, yet more strongly dissipative in the higher modes. The paper concludes that the new family of algorithms is a significant improvement over the existing methods in terms of algorithmic damping and numerical dissipation.