  The parametric degree of a rational surface is the degree of the polynomials
in the smallest possible proper parametrization. An example shows that the
parametric degree is not a geometric but an arithmetic concept, in the sense
that it depends on the choice of the ground field. In this paper, we introduce
two geometrical invariants of a rational surface, namely level and keel. These
two numbers govern the parametric degree in the sense that there exist linear
upper and lower bounds.
