  Conditional on Fourier restriction estimates for elliptic hypersurfaces, we
prove optimal restriction estimates for polynomial hypersurfaces of revolution
for which the defining polynomial has non-negative coefficients. In particular,
we obtain uniform--depending only on the dimension and polynomial
degree--estimates for restriction with affine surface measure, slightly beyond
the bilinear range. The main step in the proof of our linear result is an
(unconditional) bilinear adjoint restriction estimate for pieces at different
scales.
