A method of controlling a switching converter and a related controller suitable for the switching converter allow to implement a burst-mode functioning without generating acoustic noise and with a relevantly reduced ripple of the regulated DC voltage or current provided in output to a supplied load. The method includes sensing the difference between the error signal and the burst-stop threshold at the beginning of a burst period. If the error signal has surpassed (either upwards or downwards) the burst-stop threshold, the method sets the switching stage in a high impedance state at a new active edge of a clock signal, keeps the switching stage in the high impedance state for an integer number of cycles of the clock signal, and re-enables the switching stage to switch the energy tank circuit up to the end of the burst period. The integer number is determined based on the difference between the error signal and the burst-stop threshold.