A major disadvantage of existing methods for tuning descriptive fuzzy models is that the usual constrains over the changes on the fuzzy membership functions do not guarantee that no radical changes in the definitions and hence, no unacceptable disruptions in the interpretability of the original model would take place. This paper proposes a new tuning method, called microtuning, which avoids drastic changes by enforcing that the possible loss in interpretability is kept to minimal. This is achieved by ensuring the modified sets to have, at least, a given degree of similarity with their original. The paper focuses on the issue of how accuracy increases as the similarity constraint is relaxed. It reveals the tradeoff between losing interpretability and gaining precision in tuning a descriptive model. Simulation results show that most of the improvement in model accuracy can be obtained without major changes in the original set definitions, microtuning may be all what is required.