In this paper, we unite a controller designed via the prescribed performance control methodology, with a given, in a black box form, locally asymptotically stabilizing control scheme that encapsulates any prior knowledge related to the controlled system. In that perspective, we devise a hybrid control strategy, to guarantee the exponential convergence of the output tracking error to a prespecified neighborhood of the origin, with a predefined minimum convergence rate. Furthermore, the origin of the uncertain nonlinear error system is rendered globally asymptotically stable, while preserving the boundedness of all signals in the closed loop. Attention is paid to maintain the complexity of the resulted control solution at low levels. The developed switching logic prevents the appearance of Zeno behavior and guarantees the termination of switchings in finite time. Illustrative simulations clarify and verify the approach.