{\bf Abstract} Isometries on formal power series over the finite field $\ff_2$ or on $2$--adic integers can be computed by invertible transducers on inputs from $\{0,1\}^\infty$. We consider the structural complexity of an isometry $f$, measured as {\it tree complexity} $T(f,h)$, $h$ the tree height [H.~Niederreiter, M.~Vielhaber, {\it J.~Cpx.}, 12 ... more >>>