Let X be a Hermitian complex space of pure dimension with only isolated singularities and π : M → X a resolution of singularities. Let Ω ⊂⊂ X be a domain with no singularities in the boundary, Ω * = Ω \ Sing X and Ω ′ = π −1 (Ω). We relate L 2 -properties of the ∂ and the ∂-Neumann operator on Ω * to properties of the corresponding operators on Ω ′ (where the situation is classically well understood). Outside some middle degrees, there are compact solution operators for the ∂-equation on Ω * exactly if there are such operators on the resolution Ω ′ , and the ∂-Neumann operator is compact on Ω * exactly if it is compact on Ω ′ .