  A group of volume-preserving diffeomorphisms in 3D turns out to play a key
role in an Einstein-Maxwell theory whose Weyl tensor is selfdual and whose
Maxwell tensor has algebraically general anti-selfdual part. This model was
first introduced by Flaherty and recently studied by Park as an integrable
deformation of selfdual gravity. A twisted volume form on the corresponding
twistor space is shown to be the origin of volume-preserving diffeomorphisms.
An immediate consequence is the existence of an infinite number of symmetries
as a generalization of $w_{1+\infty}$ symmetries in selfdual gravity. A
possible relation to Witten's 2D string theory is pointed out.
