  Let Z be an Rd-valued Levy process with strong finite p-variation for some
p<2. We prove that the ''decompensated'' process Y obtained from Z by
annihilating its generalized drift has a small deviations property in
p-variation. This property means that the null function belongs to the support
of the law of Y with respect to the p-variation distance. Thanks to the
continuity results of T. J. Lyons/D. R. E. Williams, this allows us to prove a
support theorem with respect to the p-Skorohod distance for canonical SDE
driven by Z without any assumption on Z, improving the results of H. Kunita. We
also give a criterion ensuring the small deviation property for Z itself,
noticing that the characterization under the uniform distance, which we had
obtained in a previous paper, no more holds under the p-variation distance.
