As the classic transactional abstraction is sometimes considered too restrictive in leveraging parallelism, a lot of work has been devoted to devising relaxed transactional models with the goal of improving concurrency. Nevertheless, the quest for improving concurrency has somehow led to neglect one of the most appealing aspects of transactions: software composition, namely, the ability to develop pieces of software independently and compose them into applications that behave correctly in the face of concurrency. Indeed, a closer look at relaxed transactional models reveals that they do jeopardize composition, raising the fundamental question whether it is at all possible to devise such models while preserving composition. This paper shows that the answer is positive. We present outheritance, a necessary and sufficient condition for a (potentially relaxed) transactional memory to support composition. Basically, outheritance requires child transactions to pass their conflict information to their parent transaction, which in turn maintains this information until commit time. Concrete instantiations of this idea have been used before, classic transactions being the most prevalent example, but we believe to be the first to capture this as a general principle as well as to prove that it is, strictly speaking, equivalent to ensuring composition. We illustrate the benefits of outheritance using elastic trans- actions and show how they can satisfy outheritance and provide composition without hampering concurrency. We leverage this to present a new (transactional) Java package, a composable alternative to the concurrency package of the JDK, and evaluate efficiency through an implementation that speeds up state of the art software transactional memory implementations (TL2, LSA, SwissTM) by almost a factor of 3.