The concept of Lack Of Knowledge (LOK) was introduced in a previous paper in order to describe uncertainties caused by phenomena which often cannot be described, even by a properly updated model. This new theory combines convex uncertainty models with probabilistic features by introducing for each substructure two bounds of the strain energy as stochastic variables. In this paper, we discuss a general strategy of reduction of the lacks of knowledge, which consists in selecting the most relevant tests to achieve this reduction.