Building upon Brentano's (in: McAlister LL (ed) Psychology from an empirical standpoint. Routledge, London,  Brentano 1995) reintroduction of the concept of intentionality to the contemporary philosophy, Tim Crane has famously presented the intentionality as the mark of the mental. Accordingly, the problem of "intentional existence" (or rather "intentional inexistence") has resurfaced in Crane's revival of the Brentanoian theme (Crane in The objects of thought, Oxford University Press, Oxford, 2013; Aspects of psychologism, Harvard University Press, Cambridge, 2014). Here, I revise Crane's construal of Brentano's notion of intentional inexistence and reinterpret it in terms of a moderate version of relationalism. My relationalist theory of intentionality is inspired by what goes by the name of Noneliminativist Structural Realism (NSR) in the contemporary philosophy of science. NSR allows for a robust realist interpretation of the role of scientific models. The underlying insight of the paper is that it is best to be realist about the structure of the intentionality, which is the common element of the diverse theories of intentional objects. The Outcome is Structural Realist theory of Intentionality (SRI for short). I argue that SRI is not liable to the notorious objection of the impossibility of relata-less relations. I conclude that SRI fulfils the goal of robust psychological realism more economically and straightforwardly than Crane's application of the notion of models.