  We compute the deformation space of quadratic letterplace ideals $L(2,P)$ of
finite posets $P$ when its Hasse diagram is a rooted tree. These deformations
are unobstructed. The deformed family has a polynomial ring as the base ring.
The ideal $J(2,P)$ defining the full family of deformations is a rigid ideal
and we compute it explicitly. In simple example cases $J(2,P)$ is the ideal of
maximal minors of a generic matrix, the Pfaffians of a skew-symmetric matrix,
and a ladder determinantal ideal.
