Let Θ be an inner function in the upper half-plane and let K _Θ = H² Θ ΘH² be the associated model subspace of the Hardy space H². We call a nonnegative function ω Θ-admissible if in the space K _Θ there exists a nonzero function f K_Θ such that |f| ≤ ω a.e. on ℝ. We give some sufficient conditions of Θ-admissibility for the case where Θ is a meromorphic function and arg Θ grows fast ((argΘ)′ tends to infinity). Bibliography: 9 titles.