This paper considers a modified model reference adaptive control scheme that can be used to improve the transients associated with the manipulator trajectory tracking error. The improvement in transient behavior is achieved by using a modified model reference controller structure. The modification to the controller structure is motivated by treating the parameter mismatch as an external disturbance, and then designing an auxiliary control input to reject the latter. The design of the auxiliary control input uses standard results from L1 optimal control theory. Using such a modified scheme, it is shown that arbitrary improvement in transient performance is possible only if the joint accelerations are available for measurement. Otherwise, a condition involving a certain design parameter must be checked to determine if it is at all possible for the modified scheme to perform better than its unmodified counterpart. This condition does not involve the unknown robot parameters and can therefore, be easily checked a priori.