  We consider general 2D orbifold CFTs of the form M^N/S_N, with M a target
space manifold and S_N the symmetric group, and generalize the Lunin-Mathur
covering space technique in two ways. First, we consider excitations of twist
operators by modes of fields that are not twisted by that operator, and show
how to account for these excitations when computing correlation functions in
the covering space. Second, we consider non-twist sector operators and show how
to include the effects of these insertions in the covering space. We work two
examples, one using a simple bosonic CFT, and one using the D1-D5 CFT at the
orbifold point. We show that the resulting correlators have the correct form
for a 2D CFT.
