The processing of “relevant” or “meaningful” information has been related to the occurrence of macroscopic phase transitions in the system (see Jirsa (2004) [1] for a discussion). Information processing in a spatially distributed system is a function of the connectivity and the intrinsic dynamics of the elements constituting the system. The macroscopic phase transitions are influenced in particular by heterogeneous connections which connect far-distant sites. This type of connectivity is found commonly in biological systems such as the cortex. However, even before phase transitions occur, their signatures are present in a reduced variability of the timing patterns of the connected sites. Here we discuss how, and to what extent, the introduction of additional connectivity reduces the variability of timing patterns, even though the system does not perform a macroscopic phase transition.