We consider systems satisfying a matching condition that are functionally known up to weighted L-2 and L-infinity measures of uncertainty, A modified LQ measure of control and state transient performance is given, and the performance of a class of approximate-model-based adaptive controllers is studied. An upper performance bound is derived in terms of the uncertainty models (stability and the state transient bounds require only the L-2 uncertainty model; control effort bounds require both L-2 and L-infinity uncertainty models) and various structural properties of the model basis. Sufficient conditions are given to ensure that the performance is bounded independently of the model basis size.