Two possible optimization techniques for on-line adjustment of the design parameters involved in the adaptation algorithms of adaptive control schemes for minimum phase plants arc discussed. Sensitivity corrections adapled to this particular problem are introduced for correcting inaccuracies in an auxiliary model derived in order to be able to apply classical optimization techniques to the whole scheme. The main objective of such techniques is to improve the adaptation transient performances. The resulting strategies are discussed from the point of view of performance and possible implementation. Simulations illustrate the feasibility of the proposed optimizing procedures which are an extension, using a more general optimization theory and/or a sensitivity approach, of previous results and an alternative to the adaptive sampling approach of De la Sen (1984 c).