A quasi-Fuchsian 3-manifold is called almost Fuchsian if it contains an
incompressible closed minimal surface with principal curvatures in the
range of (-1,1). Such a manifold admits a foliation of parallel surfaces
which forms a path in Teichm\"uller space. The path produces an upper bound
for the Teichm\"uller distance between the two components of the conformal
boundary of the 3-manifold.