Central in this paper is a puzzling innovation project involving the introduction of a new machine in an assembly plant in the aviation industry. The project drew our attention because it achieved remarkably high performance results despite being launched with a negative business case. The observed performance trend neither corresponds to uncertainty reduction nor results from a pure investment in the unknown: we demonstrate that this case is an anomaly with regards to investment decision-making logics and learning dynamics (Learning by Doing) which traditionally explain performance gains. We find that the dynamics at work were made possible by an original and rigorous managerial approach adopted to address the significant presence of unknown at project launch and during project deployment. Based on this case study, we identify three principles respectively aiming at guiding investment decisions, at (economically) managing projects and at organizing learning in the unknown. The first principle recommends to keep using the classical economic tools (e.g. business cases) which advise against the project, but in a "diverted" way, i.e. as a means to keep the losses under control in case of failure. The second one suggests to clearly set in the team's mission the objective to discover new performance variables. The third one proposes to deploy a learning strategy related to the newly-discovered variables that is based on the very objective to build profitability and turn the project into a profitable one.