Alongside drones and Special Forces, the ‘disposition matrix’ – a kill/capture list and database – is a key device in the US government’s global ‘war on terror’, in which targeting individuals has become increasingly institutionalized. The majority of studies to date have focused on the human world of the military, insurgents and policy makers with a limited access to reliable knowledge. Using insights from technoscience and software studies, I seek here to develop a material-based perspective focusing on the neglected non-human world of software artefacts, which codify, standardize and sort our world. I will first present available knowledge about the ‘disposition matrix’ and the ‘targeting methodology’. Second, I will elaborate on the materiality of databases and data mining algorithms, showing how their technorationality is built on recombination, which fosters the production of possible future targets for a data-driven killing apparatus, in which human and non-human decision-making processes are intimately intertwined. In the third part of my article, I will discuss how computational actors make the messy targeting process more opaque and less traceable – not at least because of their underlying technorationality with its open-ended search heuristics – which advances a possibilistic, preemptive culture of technosecurity.