  We study a simple class of correlators with two heavy and two light operators
both in the D1D5 CFT and in the dual AdS$_3 \times S^3 \times T^4$ description.
On the CFT side we focus on the free orbifold point and discuss how these
correlators decompose in terms of conformal blocks, showing that they are
determined by protected quantities. On the gravity side, the heavy states are
described by regular, asymptotically AdS$_3 \times S^3 \times T^4$ solutions
and the correlators are obtained by studying the wave equation in these
backgrounds. We find that the CFT and the gravity results agree and that, even
in the large central charge limit, these correlators do not have (Euclidean)
spurious singularities. We suggest that this is indeed a general feature of the
heavy-light correlators in unitary CFTs, which can be relevant for
understanding how information is encoded in black hole microstates.
