In this paper, we investigate the tracking control problem of uncertain strict-feedback systems under deferred and asymmetric yet time-varying (DATV) constraints. We show that such type of constraints, occurring some time after (rather than from the beginning of) system operation, are frequently encountered in practice that have not been adequately addressed in existing works. By utilizing an error-shifting transformation, together with a new asymmetric Barrier Lyapunov Function with variational barrier bounds, we develop a tracking control method capable of dealing with DATV full state constraints under completely unknown initial tracking condition, leading to a control solution to the underlying problem. We also show that, with the proposed method, full state constraints being violated initially (rendering the previous methods inapplicable) can be made satisfied within a pre-specified finite time. The benefits and effectiveness of the proposed control are theoretically authenticated and numerically validated. (C) 2018 Elsevier Ltd. All rights reserved.