As an option to reduce migration from boxes of recycled paperboard into the packed food, it was proposed to apply a functional barrier layer to the internal surface of the paperboard. However, with most designs of the closures, flaps expose unprotected outer surface to the inside of the box, that is, migration may occur around the barrier, and the closures are not airtight. A pilot study provided first data on the contribution of the closures to the migration into the packed food during long‐term storage of a dry food like rice. Three closure designs were tested with the surrogates also used for determining barrier efficiency and applying the criterion that no more than 1% of the substances in the board should reach the food. Boxes were formed from paperboard with an efficient PET/PE barrier and spiked with surrogate substances. They were filled with rice and stored under various time/temperature conditions. Two closure designs represented those commonly observed for dry foods; the third avoided flaps reaching into the box by joining barrier surface against barrier surface. For the first two closure designs, migration into rice reached several per cent after just a few weeks. The third design resulted in clearly lower migration but still more than 1%. It is concluded that functional barriers on the internal surface of recycled paperboard may only reduce the migration below the proposed 1% criterion if specially designed closures are used.