In this chapter, we aim to establish that neither the current applicability, nor the future extensibility of copyright should be completely discarded in certain, well-defined cases regarding the results produced by AI. Certain aspects of the results produced by AI are already subject to copyright. At the same time, however, to enforce well-defined social interests, bringing additional sub-areas under the scope of legislation would not be without significance. Since in some situations the operation of AI may lead to serious disruptions in the functioning of the copyright markets (if it has not already done so, it may have been overlooked), it is necessary to consider the possibilities for a balanced protection of interests in situations in which AI products are competing in the market with works created by humans. To this end, extending copyright legislation and at least assessing the situations in which the results of AI compete with human creations should not be summarily discarded. A ban would not be effective. Further development of the copyright toolbox, including the creation of a new related right, could be a powerful way to strike a balance between the interests of the author and those of the AI developer and user. The chapter examines several aspects of the relationship between copyright and AI, with a particular focus on the introduction of a possible neighbouring right, which would be owned by the person using AI and would exist in respect of certain results produced with AI.