The sociological study of knowledge infrastructures and classification has traditionally focused on the politics and practices of classifying things or people. However, actors’ work to escape dominant infrastructures and pre-established classification systems has received little attention. In response to this, this article argues that it is crucial to analyze, not only the practices and politics of classification, but also actors’ work to escape dominant classification systems. The article has two aims: First, to make a theoretical contribution to the study of classification by proposing to pay analytical attention to practices of escaping classification, what the article dubs classification egress. This concept directs our attention not only to the practices and politics of classifying things, but also to how actors work to escape or resist classification systems in practice. Second, the article aims to increase our understanding of the history of quantified and statistical health surveillance. In this, the article investigates how actors in health surveillance assembled a knowledge infrastructure for surveilling, quantifying, and detecting unknown patterns of congenital malformations in the wake of the thalidomide disaster in the early 1960s. The empirical account centers on the actors’ work to detect congenital malformations and escape the dominant nosological classification of diseases, the International Classification of Diseases (ICD), by replacing it with a procedural standard for reporting of symptoms. Thus, the article investigates how actors deal with the tension between the-already-known-and-classified and the unknown-unclassified-phenomenon in health surveillance practice.