I aim to argue in favor of a phonological representation consisting not of strings, but only of ordered pairs of segments by exploring the additional power conferred by it. One goal is reducing the complexity of the representation by going from strings to directed graphs. In addition to reduplication and infixation which were already explored by Raimy (2000), other phenomena that turn out to easily follow from the additional power of this representation include at least tonal and harmony phenomena, allomorphy, and intonational phenomena. One medium-to-long term goal of this approach is to harness all the (nonsyntactic) facts of morphology and phonology into a single representation that will provide a lower bound of complexity in the Phonological component.