<p>This paper is concerned with the problem of fast accurate reference tracking for the strict-feedback systems with parametric uncertainties and unmatched disturbances. It is focused on the case where the transient response of the tracking error, except for the settling time, e.g., the overshoot, is taken into consideration in the context of ensuring the natural satisfaction of the initial condition. This significantly challenges the existing high-performance control solutions which are developed by means of the tuning function-based initialization technique, the performance funnel with an infinitely large entry, or the exponential function related to the initial tracking error. To conquer this obstruction, a novel adaptive prescribed performance control strategy is put forward in this paper. Herein, an error transformation based on a reverse tuning function is skillfully combined with the constraint-handling method to form a tight performance envelope on the tracking error. In addition, a set of self-adjustable, asymmetric and time-varying performance functions are further constructed to enhance the reliability of control designs. It turns out that the user-specified transient and steady-state tracking performance and the boundedness of all the signals in the control system are guaranteed by our approach. The above theoretical findings are substantiated via three simulation studies.</p>