The principles of an information-based approach to wrangle uncertainty are presented and applied to problems associated with the propagation of stochasticity, ignorance and numerical uncertainty. Prior knowledge that the engineer has about the model is exploited to efficiently quantify the uncertainty in the model’s output without the use of surrogate models. Indeed, the approach presented in this paper uses a simple surrogate model only during the quantification of numerical uncertainty, yet achieves model evaluation levels, typical of a surrogate-assisted uncertainty propagation effort. By carefully distinguishing between aleatory and epistemic uncertainty from characterisation to propagation, the adopted methodology provides the engineer with the means to objectively assess the trust they can put in model predictions for the intended application and to help them take evidence-based decisions. The approaches adopted in this paper are trans-probabilistic in that they utilise probability only when needed but no further and instead opt to propagate uncertainties as efficiently and appropriately as possible.