  We explore submersions introduced by reducible holonomy representations of
connections with parallel skew torsion. A submersion theorem extending previous
less general results is given. As our main application we show that parallel
3-$(\alpha,\delta)$-Sasaki manifolds admit 1-dimensional submersions onto
nearly K\"ahler orbifolds. As a secondary application we reprove that a certain
class of nearly K\"ahler manifolds submerges onto quaternionic K\"ahler
manifolds. This new proof gives an direct expression for the quaternionic
structure on the base.
