As the era of big data transforms modern medicine, clinicians have access to more health data than ever. How do medical providers determine which data are relevant to patient care, which are irrelevant, and which may be inappropriately used to justify potentially harmful interventions? One of the most prominent medical fields to address these questions head on – clinical genomics – is actively debating how to assess the value of genomic data. In-depth interviews with clinicians and a content analysis of policy documents demonstrate that while many clinicians believe that collecting as much patient data as possible will lead to better patient care, a sizeable minority of clinicians preferred to collect less data. These clinicians worried that large genomic tests provided too much data, leading to confusion and inappropriate treatment. Clinical geneticists have also started developing the concept of “actionability” to assess which types of genomic data are worth collecting and interpreting. By classifying data as useful when it can or should lead to action, clinicians can formalize and institutionalize what types of data should be ignored. But achieving consensus about what counts as “actionable” has proven difficult and highlights the different values and risk philosophies of clinicians. At the same time, many clinicians are fighting against the ignorance arising from genomic databases predominantly filled with samples from European ancestry populations. Debates about how and when to institutionalize ignorance of health data are not unique to clinical genomics, but have spread throughout many fields of medicine. As the amount of health data available to clinicians and patients grows, social science research on the politics of knowledge and ignorance should inform debates about the value of data in medicine. © 2022 The Author