Existing adaptive control algorithms at best guarantee that the tracking error is a l(2) sequence. This paper presents globally stable adaptive control algorithms for linear discrete-time systems providing l(1) tracking performance. Two algorithms with different degree of complexity are proposed, one for the case of known control directions, and a separate algorithm for the case of unknown control directions. It is demonstrated that in both cases the tracking error is l(1) sequence, while the input and output signals are uniformly bounded.