The problem studied in this paper is one of improving the performance of a class of adaptive observer in the presence of exogenous disturbances. The $H\infty$ gains of both a conventional and the newly proposed sliding-mode adaptive observer are evaluated, to assess the effect of disturbances on the estimation errors. It is shown that if the disturbance is " matched " in the plant equations, then including an additional sliding-mode feedback injection term, dependent on the plant output, improves the accuracy of observation.