Model-based testing (MBT) provides an automated approach for finding discrepancies between software models and their implementation. If we want to incorporate MBT into the fast and iterative software development process that is Continuous Integration Continuous Deployment, then MBT must be able to test the entire model in as little time as possible.However, current academic MBT tools either traverse models at random, which we show to be ineffective for this purpose, or use precalculated optimal paths which can not be efficiently calculated for large industrial models. We provide a new traversal strategy that provides an improvement in error-detection rate comparable to using precalculated paths. We show that the new strategy is able to be applied efficiently to large models. The benchmarks are performed on a mix of real-world and pseudo-randomly generated models. We observe no significant difference between these two types of models.