In this paper, we present experimental evidence from a ‘yes’/‘no’ judgement task and two acceptability rating studies (Experiments 1a-c) for the claim made in Hinterwimmer (2019) that sentences with two anaphorically interpreted complex demonstratives are less acceptable than sentences with two anaphorically interpreted definite descriptions and sentences where one of the two previously introduced referents is picked up by a complex demonstrative, while the other one is picked up by a definite description. The results of Experiment 1a and 1b are in principle compatible with the account argued for in Hinterwimmer (2019), according to which the (potentially abstract) demonstrations presupposed by demonstratives may not have overlapping trajectories. However, sentences with two anaphorically interpreted complex demonstratives are not judged as unacceptable as would be expected if they involved a presupposition violation. Therefore, we propose an alternative, economy-based pragmatic account that builds on Ahn (2019) and Nowak (2019). The question of whether the observed pattern is more compatible with the account proposed by Hinterwimmer (2019) or the alternative pragmatic account is directly addressed in a further acceptability rating study (Experiment 1c). The design of that study is similar to that of Experiment 1b, but it includes as fillers both sentences clearly violating a presupposition and sentences violating a pragmatic constraint. Since the ratings for sentences containing two anaphorically interpreted complex demonstratives are closer to the ratings for sentences violating a pragmatic constraint than for sentences violating a presupposition, we conclude that the alternative pragmatic account is preferable to the account by Hinterwimmer (2019).