Let B be a meromorphic Blaschke product in the upper half-plane with zeros Z_n and let KB - H² ⊖ BH² be the associated model subspace of the Hardy space H². A nonnegative function w on the real line is said to be an admissible majorant for K _B if there is a non-zero function f ∈ K_B such that |f| ≤ w a.e. on ℝ. We study the relations between the distribution of the zeros of a Blaschke product B and the class of admissible majorants for the space K_B.