  We address the question of whether integrable models allow for PT-symmetric
deformations which preserve their intgrability. For this purpose we carry out
the Painleve test for PT-symmetric deformations of Burgers and the Korteweg-De
Vries equation. We find that the former equation allows for infinitely many
deformations which pass the Painleve test. For a specific deformation we prove
the convergence of the Painleve expansion and thus establish the Painleve
property for these models, which are therefore thought to be integrable. The
Korteweg-De Vries equation does not allow for deformations which pass the
Painleve test in complete generality, but we are able to construct a defective
Painleve expansion.
