  We explore fermionic T-duality and self-duality in the geometry AdS3 x S3 x
T4 in type IIB supergravity. We explicitly construct the Killing spinors and
the fermionic T-duality isometries and show that the geometry is self-dual
under a combination of two bosonic AdS3 T-dualities, four fermionic T-dualities
and either two additional T-dualities along T4 or two T-dualities along S3. In
addition, we show that the presence of a B-field acts as an obstacle to
self-duality, a property attributable to S- duality and fermionic T-duality not
commuting. Finally, we argue that fermionic T-duality may be extended to CY2 =
K3, a setting where we cannot explicitly construct the Killing spinors.
