  Uranus and Neptune are still poorly understood. Their gravitational fields,
rotation periods, atmosphere dynamics, and internal structures are not well
determined. In this paper we present empirical structure models of Uranus and
Neptune where the density profiles are represented by polytropes. By using
these models, that are set to fit the planetary gravity field, we predict the
higher order gravitational coefficients $J_6$ and $J_8$ for various assumed
rotation periods, wind depths, and uncertainty of the low-order harmonics. We
show that faster rotation and/or deep winds favour centrally concentrated
density distributions. We demonstrate that an accurate determination of $J_6$
or $J_8$ with a relative uncertainty no larger than $10\%$ could constrain wind
depths of Uranus and Neptune. We also confirm that the Voyager rotation periods
are inconsistent with the measured shapes of Uranus and Neptune. We next
demonstrate that more accurate determination of the gravity field can
significantly reduce the possible range of internal structures. Finally, we
suggest that an accurate measurement of the moment of inertia of Uranus and
Neptune with a relative uncertainty of $\sim1\%$ and $\sim0.1\%$, could
constrain their rotation periods and depths of the winds, respectively.
