In this paper three new adaptive control strategies for linear discrete-time single-input/single-output plants are proposed. They enable globally stable and exponentially convergent adaptive controllers to be designed based on various approaches, such as pole placement and optimal LQ. The principle idea of the strategies proposed is to apply a fixed-parameter control law while the estimates of the plant parameters leave some appropriately chosen region. The persistency of excitation of some external signals is crucial for the stability analysis of an overall adaptive system.