For strict-feedback nonlinear systems under full-state constraints, current barrier Lyapunov function (BLF) and integral BLF based control solutions rely on feasibility conditions for virtual controllers. In this work, we present a new solution that completely removes such restrictive conditions. First, we construct a nonlinear state-dependent function that purely depends on constrained states to cope with full state and asymmetric constraints directly; second, we introduce a new coordinate transformation and integrate it into each step of dynamic surface control based backstepping design, completely circumventing the demanding feasibility conditions on virtual controllers. Consequently, there is no need for the tedious offline computations for feasibility verification, allowing the designer more freedom to select design parameters, enabling the system with a larger range of initial conditions to be handled, and rendering the solution more user-friendly in design and implementation. Simulation verification also confirms the benefits and effectiveness of the proposed control method.