Summary. The reconciliation of systems of time series subject to both temporal and contemporaneous constraints can be solved in such a way that the temporal profiles of the original series be preserved ‘at best’ (the movement preservation principle). A new feasible simultaneous reconciliation procedure is presented, which exploits the sparsity of the linear system to be solved. A two-step reconciliation strategy might be more suitable in the case of large systems. We compare the results of the simultaneous and two-step approaches for two data sets from real life.