Recently the use of a linear periodic controller has been proposed to solve the model reference adaptive control problem. The resulting controller can handle rapid changes in plant parameters, and it can provide nice transient behavior with arbitrarily good steady-state tracking using a control signal which remains modest in size. However, it also has some undesireable features: i) the proposed sampled-data controller achieves good performance by using a small sampling period, which results in large gains and a correspondingly poor noise tolerance, ii) a rapidly varying control signal is used, which may require a fast actuator, and iii) the closer to optimality that we wish to get, the more complex the controller. In this paper, we completely redesign the control law to significantly alleviate these problems; the new design provides better noise performance, especially when the sign of the high frequency gain is known, uses a smoother and smaller control signal, has a fixed complexity, independent of the desired level of performance, and is more intuitively appealing, in that probing, estimation, and control are now carried out in parallel rather than in series.