  Toom's north-east-self voting cellular automaton rule R is known to suppress
small minorities. A variant which we call R^+ is also known to turn an
arbitrary initial configuration into a homogenous one (without changing the
ones that were homogenous to start with). Here we show that R^+ always
increases a certain property of sets called thickness. This result is intended
as a step towards a proof of the fast convergence towards consensus under R^+.
The latter is observable experimentally, even in the presence of some noise.
