Forecast reconciliation for hierarchical time series involves generating base forecasts for each series in the hierarchy and then adjusting them to ensure coherence across the aggregation structure. In some applications, however, certain base forecasts must remain unchanged, or immutable, during the reconciliation process. This talk introduces a novel methodology for handling immutable forecasts by formulating reconciliation as a constrained optimisation problem that minimises the total variance of the reconciled forecast errors while satisfying equality constraints. Since it is generally not possible to preserve all base forecasts simultaneously, we derive conditions for identifying a valid set of immutable forecasts that can be maintained while ensuring coherence. An empirical application using Australian domestic tourism data demonstrates that the proposed method outperforms an existing alternative. We also briefly discuss algorithms for ensuring non-negativity of the immutable forecasts.