It is well known that for many knot classes in the 3-sphere,

any closed incompressible surface in their complements

has an essential loop which is isotopic to a loop 

on the boundary of the knot exterior.

In this paper, we investigate closed incompressible surfaces

in knot complements with this property.

We will show that for a closed incompressible surface

which is not the peripheral torus,

the slope of such the loops on the boundary of 

the knot exterior is unique,

moreover, if the slope is non-meridional,

then the surface contains the unique essential loop

up to isotopy.

A necessary and sufficient condition for knots

to bound totally knotted Seifert surfaces

is given.