The present investigation hinges on the perspective that using the most detailed computational models (e.g., very refined meshes) and/or the most complete physical models to evaluate each sample of the response is not an efficient use of computational or time resources in the presence of aleatoric uncertainty. Rather, the fidelity of the models can be degraded as long as the induced epistemic uncertainty remains small in comparison of the aleatoric uncertainty present. This perspective is here referred to as uncertainty management and the focus of the present effort is to validate this concept to two very different structures: the first is linear modeled in finite elements while the second behaves nonlinearly, is part of a multiphysics problem and is represented as a reduced order model (ROM). The reduction of fidelity and increase in computational speed is achieved in the first problem by relying on a coarse model while in the second sparsity is introduced in a large group of ROM coefficients. For these model downgrades which induce only small changes in the response, it is indeed shown that a well identified/calibrated lower fidelity model provides indeed a close fit of the random response of the higher order one. The maximum entropy nonparametric approach to uncertainty modeling is a convenient framework for this uncertainty management strategy given its capability to represent both aleatoric and some epistemic uncertainties.