By a (ρ, c, q)-wedge in the unit ball double-struck B signⁿ ⊂ ℂⁿ we mean the union of the sets double-struck B sign _ρⁿ and E_{c, q}(e₀), where double-struck B sign_ρ ⁿ = (z ∈ ℂⁿ: z ≤ ρ), 0 < ρ < 1, e₀ = 1, 0 < q < 1, ρ > 1 - (1-q)², and E_{c, q}(e₀) = (z ∈ double-struck B signⁿ: Im(1 - (z, e₀)) ≤ cRe(1 - (z, e₀)); z² - (z, e₀)² ≤ q(1 - (z, e₀)²)) (here (z, ξ) is the usual scalar product in ℂⁿ). We denote by T_a, a ∈ double-struck B signⁿ, a ≠ 0, the intersection double-struck B signⁿ and the hyperplane (z: (z, a) = a²). This paper contains a description of the sets Z of the form ∪_a∈A T_a, where A belongs to a finite union of (ρ, c, q)-wedges with 0 < q < 1/2. These sets may occur as zero-sets or interpolation sets for functions belonging to H^∞ (double-struck B signⁿ).