Let Θ be an inner function in the upper half-plane ℂ⁺ and let K _Θ denote the model subspace H ² θ Θ H ² of the Hardy space H ² = H ²(ℂ⁺). A nonnegative function w on the real line is said to be an admissible majorant for K _Θ if there exists a nonzero function f K _Θ such that f ≤ w a.e. on ℝ. We prove a refined version of the parametrization formula for K _Θ-admissible majorants and simplify the admissibility criterion (in terms of arg Θ) obtained in [8]. We show that, for every inner function Θ, there exist minimal K _Θ-admissible majorants. The relationship between admissibility and some weighted approximation problems is considered.