Cognitive diagnosis models (CDMs) have been studied as a means of providing detailed diagnostic information about the skills that have been mastered, and the skills that have not, by examinees. Prior research has examined the use of automated test assembly (ATA) alongside CDMs; however, no previous study has investigated how to perform ATA when a CDM is employed and the total amount of time taken by the test must be controlled. The purpose of the current research was to develop an ATA procedure to select tests that are highly informative while simultaneously satisfying constraints on key parameters related to the total-time distribution. In a simulation study, the procedure successfully selected tests that met these dual goals.