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Abstract We establish a framework for doing second order conformal perturbation theory for the symmetric orbifold Sym N (T 4) to all orders in N. This allows us to compute how 1/4-BPS states of the D1-D5 system on AdS 3 × S 3 × T 4 are lifted as we move away from the orbifold point. As an application we confirm a previous observation that in the large N limit not all 1/4-BPS states that can be lifted do get lifted. This provides evidence that the supersymmetric index actually undercounts the number of 1/4-BPS states at a generic point in the moduli space.