We present a new method that drastically reduces the number of the source location estimates in 3D Euler deconvolution to one only. Our method is grounded on the analytical estimators of the base level and of the horizontal and vertical source positions in 3D Euler deconvolution as a function of the x- and y-coordinates of the observations. By assuming any tentative structural index (defining the geometry of the sources), our method automatically locates on the maps of the horizontal coordinate estimates plateaus, indicating consistent estimates that are very close to the true corresponding coordinates. These plateaus are located at the neighborhood of the highest values of the anomaly and show a contrasting behavior with those estimates which form inclined planes at the anomaly borders. The plateaus are automatically located on the maps of the horizontal coordinate estimates by fitting a first-degree polynomial to these estimates in a moving-window scheme spanning all estimates. The positions where the angular coefficient estimates are closest to zero identify the plateaus of the horizontal coordinate estimates. The sample means of these horizontal coordinate estimates are the best horizontal location estimates. After mapping each plateau, our method takes as the best structural index the one which yields the minimum correlation between the magnetic and the estimated base level over each plateau. By using the estimated structural index for each plateau, our approach extracts the vertical coordinate estimates over the corresponding plateau. The sample mean of these estimates are the best depth location estimates in our method. When applied to synthetic data, our method yielded good performances even when the study area does not cover entirely the anomalies. A test on real data over intrusions in the Goiás Alkaline Province, Brazil, retrieved sphere-like sources suggesting three-dimensional bodies.