This article provides a set of general conditions to identify efficient sequential testing strategies when test information is uncertain. We first survey the Bayesian Value-of-Information (VOI) approach to test selection. Second, we extend the approach to study sequential testing systems as applied in toxicology, but also relevant in other domains. We show how the order of tests in the sequence and the stopping rule depend on prior beliefs, the diagnostic performance of tests, and testing costs. We illustrate our findings with an example from short-term genotoxicity testing and discuss implications for developing optimized sequential testing strategies for risk management of chemicals.