  We study the dynamics of a cosmological bubble wall beyond the approximation
of an infinitely thin wall. In a previous paper, we discussed the range of
validity of this approximation and estimated the first-order corrections due to
the finite width. Here, we introduce a systematic method to obtain the wall
equation of motion and its profile at each order in the wall width. We discuss
in detail the next-to-next-to-leading-order terms. We use the results to treat
the growth of spherical bubbles and the evolution of small deformations of
planar walls.
