This paper addresses the problem of parameter convergence in adaptive extremum-seeking control design. An alternate version of the popular persistence of excitation condition is proposed for a class of nonlinear systems with parametric uncertainties. The condition is translated to an asymptotic sufficient richness condition on the reference set-point. Since the desired optimal set-point is not known a priori in this type of problem, the proposed method includes a technique for generating perturbation signal that satisfies this condition in closed-loop. This demonstrates its superiority in terms of parameter convergence. The method guarantees parameter convergence with minimal but sufficient level of perturbation. The effectiveness of the proposed method is illustrated with a simulation example. (c) 2006 Elsevier Ltd. All rights reserved.