We use the best currently available estimates for interstellar parameters to update and expand the earlier study of Ratkiewicz et al. [1998>. We report (1) a more complete survey of the morphology of the heliosphere and the ways it may be modified by variation of external interstellar parameters, (2) a detailed classification of the several asymmetries and distortions associated with exterior field-flow obliquity, including cross sections of the three-dimensional structure in all three principal planes, (3) an analysis of the transition from supermagnetosonic to nearly transmagnetosonic flow, and (4) specific results for the heliosphere for the best current understanding of conditions in the local interstellar medium. ¿ 2000 American Geophysical Union