  We study the Regge limit of 4-point AdS$_3 \times S^3$ correlators in the
tree-level supergravity approximation and provide various explicit checks of
the relation between the eikonal phase derived in the bulk picture and the
anomalous dimensions of certain double-trace operators. We consider both
correlators involving all light operators and HHLL correlators with two light
and two heavy multi-particle states. These heavy operators have a conformal
dimension proportional to the central charge and are pure states of the theory,
dual to asymptotically AdS$_3 \times S^3$ regular geometries. Deviation from
AdS$_3 \times S^3$ is parametrised by a scale $\mu$ and is related to the
conformal dimension of the dual heavy operator. In the HHLL case, we work at
leading order in $\mu$ and derive the CFT data relevant to the bootstrap
relations in the Regge limit. Specifically, we show that the minimal solution
to these equations relevant for the conical defect geometries is different to
the solution implied by the microstate geometries dual to pure states.
