This article considers the complex relationship between early computer and Conceptual art in the late 1960s and early 1970s in the United States and Europe. It assesses a range of accounts that explain the simultaneous decline in art world support for computer art and growing institutional traction enjoyed by Conceptual art. The author argues that these accounts overlook a subtle but consequential difference in the aesthetic and ontological conditions of the two art forms. Comparative analysis of writings by computer and Conceptual artists and theorists ultimately shows that the relationship between the visible output and the non-visible code or algorithm in computer art is not akin to the relationship between materiality and immateriality in Conceptual art, as is oftentimes assumed. The paper suggests that historical accounts explaining the divergent trajectories of computer and Conceptual art address this difference to avoid oversimplifying computer art’s aesthetic and ontological conditions.