We study the deformation of the microscopic string theory description of the D1-D5 system away from the orbifold point and develop a programme to evaluate the anomalous dimensions of low-lying string states of the D1-D5 conformal field theory (CFT). The string state we consider belongs to the non twist sector of the CFT. We generalize the Lunin-Mathur symmetric orbifold technique and show how to compute correlation functions that contain both twist and non twist sector operators. We then perform conformal perturbation theory, investigate operator mixing at the first order in perturbation theory, and compute the mixing coefficient of the string state.