This paper addresses the fault estimation problem for discrete-time dynamic systems. First, using a specific system decomposition, we propose a new reduced-order fault estimation observer (RFEO) with multiconstrained idea. A detailed discussion of the RFEO is given. Then, with the help of the slack-variable technique, fault estimation performances are further enhanced to reduce the conservatism generated by the direct design method. Simulation results of a discrete-time aircraft application are presented to illustrate our contributions.