The Neuwirth Conjecture for a family of satellite knots

Let K be a nontrivial knot in S-3. It was conjectured that there exists a Neuwirth surface for K. That is, a closed surface in S-3 containing the knot K as a nonseparating curve and such that every compressing disk for the surface intersects the knot in at least two points. We provide explicit constructions of Neuwirth surfaces for a family of satellite knots, which do not depend on the existence of nonorientable algebraically incompressible and partial derivative-incompressible spanning surfaces for these knots.