  We consider the height process of a Levy process with no negative jumps, and
its associated continuous tree representation. Using Levy snake tools developed
by Duquesne and Le Gall, with an underlying Poisson process, we construct a
fragmentation process, which in the stable case corresponds to the self-similar
fragmentation described by Miermont. For the general fragmentation process we
compute a family of dislocation measures as well as the law of the size of a
tagged fragment. We also give a special Markov property for the snake which is
interesting in itself.
