For a class I of multivariable, nonlinearly-perturbed, linear, minimum-phase systems of relative degree one, with output measurement noise of Sobolev class W1,infinity (absolutely continuous on compact intervals, and bounded with essentially bounded derivative), the following servomechanism problem is solved. Determine a I-universal adaptive strategy to control the output to track any reference signal in W1,infinity, with tracking error asymptotic to a ball of arbitrary prescribed radius lambda>0. The control strategy is simple and does not invoke an internal model principle.