With the aim to preserve deadlock freedom, we define a new refinement preorder for modal transition systems (MTSs), using an MTS-specific variant of testing inspired by De Nicola and Hennessy. We characterize this refinement with a kind of failure semantics and show that it “supports itself,” for example, in the sense of thoroughness—in contrast to standard modal refinements. We present a conjunction operator with respect to our new refinement, which is quite different from existing ones. It always returns an MTS—again in contrast to the case of modal refinement. Finally, we also consider De Nicola’s and Hennessy’s may- and must-testing, where the latter leads to a semantics that is also compositional for hiding.