The measurement of the Baryon Acoustic Oscillation (BAO) feature imprinted in the clustering distribution of galaxies is becoming a mainstream method for large galaxy surveys to determine the relation between distance and redshift. However, obtaining precise determinations of the distance-redshift relation requires a low uncertainty in the position of the BAO, which is usually achieved by extending the survey to probe a larger volume. In this talk I will describe how a simple method dubbed "reconstruction" is able to reduce the uncertainties in these measurements by partially undoing the effects of non-linear evolution responsible of washing away the BAO. The reduction in the error bar is therefore given for free, without the need for further additional observations, since the method uses information from the density field that is not captured by two-point clustering statistics. I will describe how reconstruction has successfully been applied for the first time this year to the LRG and CMASS galaxy samples from Sloan Digital Sky Survey, and how cosmological constraints benefit from these high-precision BAO measurements.