Method for controlling an accumulating device (buffer) having a number of tracks each of which defines at least one accumulation segment along which may be arranged sets of postal items partially overlying each other (shingled). One first section and one second section are defined as including, respectively, one first and one second sub-set of tracks designed to communicate at output, through singling devices, with sorting devices. For each section, successive phases of accumulation and unloading are carried out, thus achieving with great efficiency the unloading of postal items towards sorting devices, and thus enabling the handling of a large number of postal items towards the highest possible number of destinations.