It is shown in the paper that the utilization of proportional + integral adaptation (2.5) allows us to establish conditions for global stability in the face of unmodeled dynamics of a control scheme which incorporates a mechanism to freeze the parameter at arbitrary rates. Adaptive controllers with continuous or periodic updating of the parameter estimates are derived as particular cases of the proposed scheme. From a practical stand point, the controller may overcome the lack of robustness of purely continuous algorithms due to the infinite "bandwidth" of the parameter adjustment. Furthermore, it gives the designer an additional degree of freedom to improve the systems response. Interestingly enough, the conditions for global stability coincide with the ones required in [1].