This paper is concerned with global stabilization of discretetime multiple integrators with bounded controls by utilizing the energy function based approach. First, a discrete-time double integrators system subject to input additive disturbances is stabilized by a bounded feedback whose formula involves a linear function of the state and a saturation function only. Next, this result is used to stabilize a discrete-time multiple integrators of arbitrary length by bounded control with the aid of a special canonical form. Compared with the existing results, the proposed controllers require fewer saturation functions, which allow a better use of the control energy. Moreover, some free parameters that are introduced into these controllers can help improve the transient performance of the closed-loop systems significantly. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.