  The hyper-CR Einstein-Weyl structures on $\R^3$ can be described in terms of
the solutions to the dispersionless Hirota equation. In the present paper we
show that simple geometric constructions on the associated twistor space lead
to deformations of the Hirota equation that have been introduced recently by B.
Kruglikov and A. Panasyuk. Our method produces also the hyper-CR equation and
can be applied to other geometric structures related to different twistor
constructions.
