  We introduce two numerical invariants, the waist and the trunk of knots. The
waist of a closed incompressible surface in the complement of a knot is defined
as the minimal intersection number of all compressing disks for the surface in
the 3-sphere and the knot. Then the waist of a knot is defined as the maximal
waist of all closed incompressible surfaces in the complement of the knot. On
the other hand, the trunk of a knot is defined as the minimal number of the
intersection of the most thick level 2-sphere and the knot over all Morse
positions of the knot. In this paper, we obtain an inequality between the waist
and the trunk of knots and show that the inequality is best possible. We also
define the supertrunk of a knot and relate it to the hull number and the
3-width.
