  We prove the Bernoulli property for a class of counter-twisting linked twist
maps. These compose orthogonal linear shears on the torus, orientated in the
opposite sense to their co-twisting counterparts (where the shears reinforce
one another). Compared to previous studies we focus on the parameter space
corresponding to weak shears, near the critical parameter below which
hyperbolicity is lost and the map is non-mixing. The approach developed to deal
with this situation appears applicable to a broad range of non-uniformly
hyperbolic examples.
