  Consider an immersed Legendrian surface in the five dimensional complex
projective space equipped with the standard homogeneous contact structure. We
introduce a class of fourth order projective Legendrian deformation called
\emph{$\,\Psi$-deformation}, and give a differential geometric characterization
of surfaces admitting maximum three parameter family of such deformations. Two
explicit examples of maximally $\, \Psi$-deformable surfaces are constructed;
the first one is given by a Legendrian map from $\, \PP^2$ blown up at three
distinct collinear points, which is an embedding away from the -2-curve and
degenerates to a point along the -2-curve. The second one is a Legendrian
embedding of the degree 6 del Pezzo surface, $\, \PP^2$ blown up at three
non-collinear points. In both cases, the Legendrian map is given by a system of
cubics through the three points, which is a subsystem of the anti-canonical
system.
