Totally stably tame variables

We improve the constructions of [Ann. Polon. Math. 76 (2001) 67] to obtain new automorphisms and variables of A[x,y]. We introduce the concept of totally stably tame variables. This allows us to prove that all our variables are stably tame. Comparing different notions of length, we show that some of our variables are not in Berson's class (cf. [J. Pure Appl. Algebra 170 (2002) 131] for definition).