Many health claims whose authorisation the food industry had hoped would not cause any problems, have found no grace before the European Food Safety Authority (EFSA). Amongst the different grounds for rejection, which are often inadequately explained, one stands out, namely “lack of precision” regarding the health relationship. Such claims that have been negatively evaluated by EFSA are not authorised by the European Commission. The authors present an option whereby these EFSA-assessed, unauthorised health claims can be used for the marketing of foods in practice, provided the relevant products contain vitamins or minerals or other substances for which health claims have been authorised.