  We consider the D1D5 CFT near the orbifold point and develop methods for
computing the mixing of untwisted operators to first order by using the OPE on
the covering surface. We argue that the OPE on the cover encodes both the
structure constants for the orbifold CFT and the explicit form of the mixing
operators. We show this explicitly for some example operators. We start by
considering a family of operators dual to supergravity modes, and show that the
OPE implies that there is no shift in the anomalous dimension to first order,
as expected. We specialize to the operator dual to the dilaton, and show that
the leading order singularity in the OPE reproduces the correct structure
constant. Finally, we consider an unprotected operator of conformal dimension
(2,2), and show that the leading order singularity and one of the subleading
singularies both reproduce the correct structure constant. We check that the
operator produced at subleading order using the OPE method is correct by
calculating a number of three point functions using a Mathematica package we
developed. Further development of this OPE technique should lead to more
efficient calculations for the D1D5 CFT perturbed away from the orbifold point.
