For switching functions $f$ let $C(f)$ be the combinatorial complexity of $f$. We prove that for every $\varepsilon greater than 0$ there are arbitrarily complex functions $f:{0,1}^{n} \rightarrow {0,1}^{n}$ such that $C(fxf) \leq (1+ \varepsilon) C(f)$ and arbitrarily complex functions $g:{0,1}$ such that $C(v c(fxf)) \leq (1 + \varepsilon)C(f)$. These results and the techniques developed to obtain them are used to show, that Ashenhurst decomposition of switching functions does not always yield optimal circuits and to prove a new result concerning the trade-off between circuit size and monotone circuit size.