This technical note tackles the problem of constructing state-feedback stabilizers that guarantee good transient closed-loop performance when applied to general unknown nonlinear multiinput state-feedback stabilizable systems. An adaptive Control Lyapunov Function-based control scheme is proposed in order to address this problem. Mathematical analysis establishes that the proposed control scheme guarantees good closed-loop transient performance outside the regions where the system is uncontrollable, provided the controlled system admits a controllability-like property.