  We consider a subclass of bipartite CHSH-type Bell inequalities. We
investigate operations, which leave their Tsirelson bound invariant, but change
their classical bound. The optimal observables are unaffected except for a
relative rotation of the two laboratories. We illustrate the utility of these
operations by giving explicit examples: We prove that for a fixed quantum state
and fixed measurement setup except for a relative rotation of the two
laboratories, there is a Bell inequality that is maximally violated for this
rotation, and we optimise some Bell inequalities with respect to the maximal
violation. Finally we optimise the qutrit to qubit ratio of some dimension
witnessing Bell inequalities.
