Data is on the tip of everyone’s tongue, but what does it mean and what does it want from us? This paper critically reflects on a series of codesign workshops that engaged participants in imagining alternatives to dominant narratives about data concerning public surveillance (2014-2016), climate change (2017-2018) and women’s health (2019-ongoing). The theoretical ambition of the workshops, titled Myths of the Near Future (2014-2016) and Expanding Experimental Aesthetics in the Social Imaginary (2018-ongoing), was to explore the interpretation of data through codesign with approaches that aim to reverse this method’s tendency to limit the volition of participants. The paper first describes my rationale for structuring the workshop activities to misuse technologies for the purpose of collaboratively reinterpreting common fears, fantasies and phobias about data. Countering the potential of codesign to facilitate participation and user engagement, and flip into its opposite, coercion and the disempowerment of participants, the paper offers a preliminary account of my testing of an advanced form of codesign, ethnographic surrealism. Drawing from Michel Leiris’s exploration of subjectivity in ethnographic surrealism I describe how the iterative development of the workshops has supported the production of images and narratives that are aesthetically charged, expanding opportunities for reflection, co-creation and coexistence relevant to creative practitioners in achieving the often-touted altruistic objectives of codesign.