Irreversible deformation of paper is a challenge for both printer operation and product quality, particularly in inkjet printing with water-based inks. Here we are investigating permanent paper curl, which is the residual curl of paper after drying of the ink (i.e., it is not the immediate paper curl due to wetting). The key aim of this work was to test the hypothesis that permanent paper curl is created by partial opening and rearrangement of the fibre–fibre bonds in the wetted paper layer. In order to test this hypothesis, we produced paper with crosslinked fibre–fibre bonds that do not open in the presence of water. Polyamideamine epichlorohydrin (PAE) and 1,2,3,4-butanetetracarboxylic acid were used as crosslinking agents and properties of the treated paper samples were analysed. Both agents led to significantly improved wet strength of the papers, furthermore we indeed found that the permanent curl of crosslinked papers was strongly reduced. Other curl related mechanisms like differences in fibre swelling, paper hydroexpansion and liquid penetration were not able to explain the reduction in curl. The finding that the creation of fibre–fibre bonds unaffected by water prevents permanent curl of paper after wetting and redrying leads to the conclusion that the mechanism for creating permanent paper curl after wetting is related to the partial opening and rearrangement of fibre–fibre bonds in the wetted paper. Possible pathways to apply these findings to paper production are discussed, for example switchable or temporary wet strength agents.