Exascale systems will suffer failures hourly. HPC programmers rely mostly on application-level checkpoint and a global rollback to recover. In recent years, techniques reducing the number of rolling back processes have been implemented via message logging. However, the log-based approaches have weaknesses, such as being dependent on complex modifications within an MPI implementation, and the fact that a full restart may be required in the general case. To address the limitations of all log-based mechanisms, we return to checkpoint-only mechanisms, but advocate data-flow-driven recovery (DFR), a fundamentally different approach relying on analysis of the data flow of iterative codes, and the well-known concept of data-flow graphs. We demonstrate the effectiveness of DFR for an MPI stencil code to optimise rollback and reduce the overall energy consumption by 10-12 % on idling nodes during localised rollback. We also provide large-scale estimates for the energy savings of DFR compared to global rollback, which for stencil codes increase as n square for a process count n.