  We study supergravity instantons sourced by axion (and saxion) fields in the
Euclidean $AdS_3\times S^3 \times CY_2$ vacua of IIB supergravity. Such
instantons are described by geodesic curves on the moduli space; the timelike
geodesics can describe Euclidean wormholes, the lightlike geodesics describe
(generalisations of) D-instantons and spacelike geodesics are sub-extremal
versions thereof. We perform a concrete classification of such geodesics and
find that, despite earlier claims, the wormholes fail to be regular. A subclass
of the lightlike geodesics is supersymmetric and, up to dualities, lift to
Euclidean strings wrapping 2-cycles in the CY$_2$. The dual of these instantons
are expected to be worldsheet instantons of the D1-D5 CFT.
