  One of the fundamental distinctions in McMullen and Sullivan's description of
the Teichm\"uller space of a complex dynamical system is between discrete and
indiscrete grand orbit relations. We investigate these on the Fatou set of
transcendental entire maps and provide criteria to distinguish between the two
types. Furthermore, we show that discrete and indiscrete grand orbit relations
may coexist non-trivially in a wandering domain, a phenomenon which does not
occur for any other type of Fatou component. One of the tools used is a novel
quasiconformal surgery technique of independent interest.
