Fairness considerations are a strong motivational force in social decision-making. Here, we investigated the role of intentionality in response to unfair offers in the Ultimatum Game by manipulating both proposers' degree of control over the selection of offers and the context pertaining to the outcomes of offers proposers can choose from. As a result, the design enabled us to disentangle intention- and context-based decision-making processes. Rejection rates were higher when an unfair offer was intentionally chosen over a fair alternative than when it was chosen by the computer, outside proposers' control. This finding provides direct evidence for intention-based decision-making. Also, rejection rates in general were sensitive to the context in which an offer was made, indicating the involvement of both intention- and context-based processes in social decision-making. Importantly, however, the current study highlights the role of intention-based fairness considerations in basic decision-making situations where outcomes are explicitly stated and thus easy to compare. Based on these results, we propose that fairness can be judged on different, but additive levels of (social-) cognitive processing that might have different developmental trajectories.