  We use the procedure of reduction of Courant algebroids to reduce strong KT,
hyper KT and generalized Kaehler structures on Courant algebroids. This allows
us to recover results from the literature as well as explain from a different
angle some of the features observed there in. As an example, we prove that the
moduli space of instantons of a bundle over a SKT/HKT/generalized K\"ahler
manifold is endowed with the same type of structure as the original manifold.
