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Since the Voyager fly-bys of Uranus and Neptune, improved gravity field datahave been derived from long-term observations of the planets' satellitemotions, and modified shape and solid-body rotation periods were suggested. Afaster rotation period (-40 min) for Uranus and a slower rotation period(+1h20) of Neptune compared to the Voyager data were found to minimize thedynamical heights and wind speeds. We apply the improved gravity data, themodified shape and rotation data, and the physical LM-R equation of state tocompute adiabatic three-layer structure models, where rocks are confined to thecore, and homogeneous thermal evolution models of Uranus and Neptune. Wepresent the full range of structure models for both the Voyager and themodified shape and rotation data. In contrast to previous studies based solelyon the Voyager data or on empirical EOS, we find that Uranus and Neptune maydiffer to an observationally significant level in their atmospheric heavyelement mass fraction Z1 and nondimensional moment of inertia, nI. For Uranus,we find Z1 < 8% and nI=0.2224(1), while for Neptune Z1 < 65% and nI=0.2555(2)when applying the modified shape and rotation data, while for the unmodifieddata we compute Z1 < 17% and nI=0.230(1) for Uranus and Z1 < 54% andnI=0.2410(8) for Neptune. In each of these cases, solar metallicity models(Z1=0.015) are still possible. The cooling times obtained for each planet aresimilar to recent calculations with the Voyager rotation periods: Neptune'sluminosity can be explained by assuming an adiabatic interior while Uranuscools far too slowly. More accurate determinations of these planets' gravityfields, shapes, rotation periods, atmospheric heavy element abundances, andintrinsic luminosities are essential for improving our understanding of theinternal structure and evolution of icy planets.

New indication for a dichotomy in the interior structure of Uranus and Neptune from the application of modified shape and rotation data