We introduce a process calculus with a new prefixing operator that allows us to model locally controlled reversibility. Actions can be undone spontaneously, as in other reversible process calculi, or as pairs of concerted actions, where performing a weak action forces undoing of another action. The new operator in its full generality allows us to model out-of-causal order computation, where causes are undone before their effects are undone, which goes beyond what typical reversible calculi can express. However, the core calculus, which uses only the reduced form of the new operator, is well behaved as it satisfied causal consistency. We demonstrate the usefulness of the calculus by modelling the hydration of formaldehyde in water into methanediol, an industrially important reaction, where the creation and breaking of some bonds are examples of locally controlled out-of-causal order computation.