One of the fundamental aspects of quantum control is the identification of the optimal field to be applied to the system to be controlled in order to find an optimal targeting strategy. In the case of an open quantum system, this is only possible if the system-bath interaction is properly taken into account. There are however cases where such a precise knowledge turns out not to be necessary. In such scenarios, the so-called fixed-dissipator approach can be successfully applied. By analysing the case of a single quit driven by an external laser, the limits of this approximation are studied comparing the results with the ones obtained by microscopic derivation of the master equation.