A method for balancing rotating machinery, such as gas turbine engines, to minimize vibrations. The method involves operation of the engine for a period of time at varying power levels and ranges of other operational parameters representative of the system operating envelope to obtain vibration data (amplitude and phase) for the full range of dynamic responses of interest. This usually includes time at elevated power settings until the engine reaches thermal stability, altitude variation, etc. as well as the full engine operating range. The full set of vibration data measured during the engine run is analyzed to generate unique unbalance states. The unique unbalance states are then analyzed and the mean unbalance state is identified. Balancing masses can then be installed or removed in accordance with a balance solution that is equal and opposite to the mean unbalance state.