Polymers made from zwitterionic repeat units (bearing no net charge) have intriguing solution properties, especially in contrast to polyelectrolytes, such as an apparent indifference to salt concentration. These polyzwitterions (PZs) have come under renewed scrutiny because of their use in high performance antifouling coatings. Here, an amidosulfobetaine polymer was used to shed light on the complex and poorly understood response of PZ solution conformation to ionic strength. A Hofmeister anion series NaX, where X = SO42-, Cl-, Br-, NO3-, ClO4-, and SCN-, provided a systematic way to tune PZ/ion interactions. A consistent picture of PZ conformation emerged, where the role and location of counterions (how they pair with the polymer chain) depend on their position in the Hofmeister series. At least four regimes of PZ conformation/interaction as a function of ionic strength were observed, the Iast showing no change in coil size (hydrodynamic radius) as a function of ionic strength for all monovalent salts in the concentration range 0.6-4 M. Hydrophobic (less hydrated) anions ClO4- and SCN- yielded a clear minimum in coil size at lower [NaX], whereas PZ in solutions of hydrophilic ions SO42- and Cl- showed only a hint of the much-discussed "anti-polyelectrolyte" expansion of PZ with increasing [NaX]. Static light scattering results, when analyzed using Stockmeyer's theory of scattering from multicomponent systems, revealed that NaX is associated with PZ with a corresponding increase in apparent molecular weight. Static light scattering measurements at low [NaX] show solution ions are excluded from PZ coils dressed with hydrophobic NaX. Dynamic light scattering in salt-free solutions at elevated temperatures revealed substantial chain stiffening of PZ, thought to be caused by nearest-neighbor interactions between zwitterion groups. DLS yielded a fast mode in these salt-free solutions, ascribed to soliton-like transport of waves of associated zwitterionic groups along the PZ backbone.