In this paper, consideration is given of the role of register in atonal counterpoint, a topic neglected in many models of post-tonal polyphony. Contrapuntal progressions are compared against two types of symmetry, contrary motion symmetry and parallel motion symmetry; the amount a progression deviates from contrary motion symmetry is termed its divergence, the amount a progression deviates from parallel motion symmetry is termed its skewness. The cumulative effects of the two asymmetry measures are explored in an analysis of a passage from the Sonata for Violin by Roger Sessions. In addition, a graph model for exploring these asymmetries is proposed, and new counterpoints are derived from given ones by holding skewness structure invariant while modifying the divergence structure, and vice-versa. Other musical situations in which similar techniques can be utilized are also examined.