  We critically evaluate the most widespread assumption in the theoretical
description of coherent control strategies for open quantum systems. We show
that, for non-Markovian open systems dynamics, this fixed-dissipator assumption
leads to a serious pitfall causing insurmountable difficulties in the effective
modelling of the controlled system. We show that the only way to avoid these
problems is a full microscopic description of the controlled system in presence
of noise. We illustrate our findings with a paradigmatic example.
