Disclosed is a method and apparatus for performing Dynamic Element Matching (DEM). The method operates to input a plurality of digital values and, for each value, to generate a plurality of N signals individual ones of which are intended to drive one of a plurality of N elements. The plurality of signals are generated so as to average the usage of individual ones of the N elements over time. The method further periodically rearranges the plurality of N signals so as to suppress the generation of undesired periodicities or tones in the usage of the N elements, and without affecting the averaging of the usage of the N elements. Preferably the periodic rearrangement occurs only at a time when the usage of the N elements is indicated as being averaged using, for example, an enable signal that is input to a secondary DEM block from a primary DEM block. The plurality of N signals are preferably generatd by the primary DEM block using a cyclic DEM algorithm, such as a Data Weighted Averaging (DWA) algorithm or a rotation-based Clocked Averaging (CLA) algorithm, and the periodic rearrangment performed by the secondary DEM block is preferably based on randomization or pseudo-randomization.