  Following recent claims relative to the question of large anisotropy
production in regular bouncing scenarios, we study the evolution of such
anisotropies in a model where an Ekpyrotic phase of contraction is followed by
domination of a Galileon-type Lagrangian which generates a non-singular bounce.
We show that the anisotropies decrease during the phase of Ekpyrotic
contraction (as expected) and that they can be constrained to remain small
during the non-singular bounce phase (a non-trivial result). Specifically, we
derive the e-folding number of the phase of Ekpyrotic contraction which leads
to a present-day anisotropy in agreement with current observational bounds.
