The measurement of the betatron tunes in a circular accelerator is of paramount importance due to their impact on beam dynamics. The resolution of the these measurements, when using turn-by-turn (TBT) data from beam position monitors, is greatly limited by the available number of turns in the signal. Because of decoherence from finite chromaticity and/ or amplitude detuning, the transverse betatron oscillations appear to be damped in the TBT signal. On the other hand, an adequate number of samples is needed, if precise and accurate tune measurements are desired. In this paper, a method is presented that allows for very precise tune measurements within a very small number of turns. The theoretical foundation of this method is presented with results from numerical and tracking simulations and experimental TBT data which are recorded at electron and proton circular accelerators.