  We study the spectrum of certain two-particle operators in the supergravity
regime of the D1-D5 system, focussing on the four-point correlators of tensor
multiplets on $AdS_3\times S^3$ at tree level. In Mellin space, these are
nicely determined by a single amplitude, which makes manifest the large $p$
limit, the connection with the flat space S-matrix, and the six dimensional
conformal symmetry. We compute the $(1,1)\times \overline{(1,1)}$
superconformal blocks for the two-dimensional $\mathcal{N}=(4,4)$ conformal
theory at the boundary, and then we obtain a formula for the anomalous
dimensions of the operators exchanged in the symmetric and anti-symmetric
flavor channels. These anomalous dimensions solve an unmixing problem which is
analogous to the one in $AdS_5\times S^5$, with interesting modifications.
Along the way we show how the $(1,1)\times \overline{(1,1)}$ superconformal
blocks relate to those in $\mathcal{N}=4$ SYM in four dimensions, and we
provide new intuition on the known data for $AdS_5\times S^5$.
