The promised merits of data-driven innovation in general and algorithmic systems in particular hardly need enumeration. However, as decision-making tasks are increasingly delegated to algorithmic systems, this raises questions about accountability. These pressing questions of algorithmic accountability, particularly with regard to data-driven innovation in the public sector, deserve ample scholarly attention. Therefore, this paper brings together perspectives from governance studies and critical algorithm studies to assess how algorithmic accountability succeeds or falls short in practice and analyses the Dutch System Risk Indication (SyRI) as an empirical case. Dissecting a concrete case teases out to which degree archetypical accountability practices and processes function in relation to algorithmic decision-making processes, and which new questions concerning algorithmic accountability emerge therein. The case is approached through the analysis of “scavenged” material. It was found that while these archetypical accountability processes and practices can be incredibly productive in dealing with algorithmic systems they are simultaneously at risk. The current accountability configurations hinge predominantly on the ex ante sensitivity and responsiveness of the political fora. When these prove insufficient, mitigation in medias res/ex post is very difficult for other actants. In part, this is not a new phenomenon, but it is amplified in relation to algorithmic systems. Different fora ask different kinds of medium-specific questions to the actor, from different perspectives with varying power relations. These algorithm-specific considerations relate to the decision-making around an algorithmic system, their functionality, and their deployment. Strengthening ex ante political accountability fora to these algorithm-specific considerations could help mitigate this.