Angluin algorithm L* is a well known approach for learning unknown models as minimal deterministic finite automata (DFA) in polynomial time. It uses concept of oracle which presumably knows the target model and comes up with a counterexample, if the conjectured model is not correct. This algorithm can be used to infer the models of software artefacts and a cheap oracle for such components uses random strings (built from inputs) to verify the inferred models. In such cases and others the provided counterexamples are rarely minimal. The length of the counterexample is an important parameter to the complexity of the algorithm. The proposed technique tends to reduce the impact of non minimal counterexamples. The gain of the proposed algorithm is confirmed by considering a set of experiments on DFA learning.